I don’t know if this type of measurement would be useful, but if you have 1 2 3 4 3 2 1 2 3 4 3 2 1, the 2’s would be closer together and then farther apart. And the 3’s would be closer together and then farther apart. Maybe for each symbol, find the positions and the distances between each, alternating distances. If the odd distances are generally smaller than the even distances, or vice versa, generally for some symbols, then maybe the measurements all added up would be different than for perfect regular cycles. Jarlve, you probably already thought of something like that.
Not really, I’ll get on it.
Something rather quickly.
A higher score is more indicative of distance alternation. This was a very good idea smokie. Based on this it may seem that we could softly rule out the 340 as palindromic because it sits even lower than smokiepalindromic2 which has *only* 8 such cycles. Also, the "+" symbol has a good amount of distance alternation and thus is probably inflating the score (+5.4) since it is hard to imagine it being part of a palindromic cycle.
A quick collection of ciphers: 340: 50.2911484528144 408 (340 character part): 37.27994573375139 smokiepalindromic1: 82.46742178610356 <--- smokiepalindromic2: 58.14505154251292 smokie1: 40.18910958766008 smokie2: 35.73507922002787 smokie3: 44.95149420984569 smokie4: 47.21324590572822 moonrock1: 43.74078836872795 doranchak1: 40.42062118697717 doranchak2: 44.39644610983818 gardi: 42.17268658815245 alisowky: 52.35642277575229 daikon1: 49.95212861957725 glurk1: 42.82069942273643 ccactus: 52.79750597718509 tonyb1: 56.86402909935718 largo4: 46.31936106068846 validator: 60.6173189060187
Note that I did not factor in the actual distance between each symbol. It may be worth doing so, but the 340 has some symbols that have tremendous distance gaps between them which can be seen in an image I uploaded a few of my posts above.
I ran another cycle-finding experiment. The approach considers a set of symbols and removes all symbols from the cipher that are not in that set. For example, in Z408, let’s pick symbols +, 6, W and Z. If we remove all other symbols, the resulting cipher string is: ZW+6ZW+6ZW+6ZW+6ZW+6ZW++WZ6Z+W6W6. Then, I detect the longest repeating pattern within the resulting string. In our example the pattern is ZW+6 and it occurs 5 times in a row: [ZW+6] [ZW+6] [ZW+6] [ZW+6] [ZW+6] ZW++WZ6Z+W6W6.
The benefit of this approach is that longer patterns are detected. For example, in Z340, if you pick symbols *, B, 6 and t, you get this string: B*B*t [*B6BtB] [*B6BtB] *B6BtBB*. WIthin that string, the pattern *B6BtB occurs twice in a row. But are these observations significant?
To estimate significance, I ran shuffle tests, and counted how often patterns of length A occur B times in a row within strings of length C. For example, the pattern *B6BtB has length 6, 2 occurrences, and full string length 25. In 3407 shuffles of Z340, I found 130 patterns of length 6 with 2 repeats in string length of 25. So the estimated probability of a pattern like *B6BtB happening twice in a string of length 25 is 130/3407 = 0.0382. (Note: There are only 3407 shuffles due to how long it takes to brute force search for cycles for all combinations of 4 symbols).
I ran the experiment for z340 and z408, for L=2 through L=4, and here are the combined results sorted by the estimated probabilities:
https://docs.google.com/spreadsheets/d/ … sp=sharing
I excluded all results that had an estimated probability greater than or equal to 1.
Unsurprisingly, Z408’s patterns dominate the top of the list due to their strength. But I was surprised that the most significant pattern from Z340 was ++F+FF+++++F++F which occurs twice in the full string +++++F+FF+++++F++F++F+FF+++++F++F+. In fact, four unusual patterns (seen at the top in the excerpt below) are found to be more significant than the lM pattern which has a perfect cycle of 7 occurrences.
z340 2 ++F+FF+++++F++F 15 2 +++++F+FF+++++F++F++F+FF+++++F++F+ 34 7.06 1291979 0.0010557447 z340 4 *B6BtB 6 3 B*B*t*B6BtB*B6BtB*B6BtBB* 25 25.92 3407 0.004109187 z340 4 MlMFFlF>MFlF 12 2 >lMlMFFlF>MFlFMlMFFlF>MFlF>M 28 13.71 3407 0.0044027003 z340 4 MlMFFlFXMFlF 12 2 lMlMFFlFXMFlFMlMFFlFXMFlFM 26 14.77 3407 0.00528324 z340 2 lM 2 7 lMlMlMlMlMlMlM 14 98.00 1291979 0.005793438 z340 3 MlMFFlFMFlF 11 2 lMlMFFlFMFlFMlMFFlFMFlFM 24 11.00 63860 0.007907923 z340 4 ^2cc( 5 3 ^2(c(^2^2(2c(22c^2cc(^2cc(^2cc(c 32 16.88 3407 0.008511887 z340 4 K++O+KO++++Z 12 2 +OK+ZO++K++O+KO++++ZK++O+KO++++Z+KO++++OOZOK+ 45 8.53 3407 0.009685941 z340 3 EBBSBB 6 3 EBBSBBEBBSBBEBBSBBS 19 25.58 63860 0.009818353 z340 3 ++K++O+KO++ 11 2 +OK+O++K++O+KO++++K++O+KO+++++KO++++OOOK+ 41 6.44 63860 0.012934544 z340 4 ++O-+O++++Z- 12 2 +O+ZO++++O-+O++++Z-++O-+O++++Z-+O++++OO-ZO+ 43 8.93 3407 0.014382155 z340 4 +B+|B2+ 7 2 |2+BB+++2+|+2+2|2++++2B++B+|B2|+B+|B2++B+|B2++B|++|BB|+ 55 4.07 3407 0.017904315 z340 3 B2Bz 4 3 2BBz2z22z2z2BzBB2BzB2BzB2BzBBz 30 10.80 63860 0.01954275 z340 4 +B+|BR+ 7 2 R|+BB+++R+|+R+|++++RB++B+R|BR|+B+|BR++B+|BR++B|++|BB|+ 54 4.15 3407 0.019958908 z340 4 ++++zOp 7 2 pp+O+zpppO+++z+pO+zO+z+++z++Op+pO+z++++zOp++++zOpOpzO+ 54 4.15 3407 0.019958908 z340 4 ++V++++&+;V++ 13 2 V++V++++&+;V++++V++++&+;V++V+++++;+ 35 11.89 3407 0.021719988 z340 2 2z 2 6 2z2z22z2z2z2z2z2zz 18 48.00 1291979 0.02199881 z340 4 ++ZV++++&+V++ 13 2 V++ZV++++&+V++++ZV++++&+V++VZ+++++Z+ 36 11.56 3407 0.022600528 z340 3 V|c 3 4 V|cV|cV|cV|c||ccVV|cc|c|c| 26 22.15 63860 0.023081742 z340 4 ++ZV+++++;V++ 13 2 V++ZV+++++;V++++ZV+++++;V++VZ+++++Z;+ 37 11.24 3407 0.027883768 z340 4 K/DK; 5 3 DKK/DK;K/DK;K/DK; 17 31.76 3407 0.027883768 z340 2 KM 2 6 KMKMKMKMKMKMMK 14 61.71 1291979 0.029413791 z340 4 DKZK/ 5 3 DKZK/DKZK/DKZK/DZK 18 30.00 3407 0.029644849 z340 3 KOM 3 4 OKMOKMOKOMKOMKOMKOMOOMOK 24 24.00 63860 0.032492954 z340 3 ++O-+O++++- 11 2 +O+O++++O-+O++++-++O-+O++++-+O++++OO-O+ 39 6.77 63860 0.033041026 z340 3 ++Fy 4 3 +y++++F+FF+++++Fy++Fy++Fy+FF++y+++F++F+ 39 8.31 63860 0.033996243 z340 4 DKfZK 5 3 DKfZKDKfZKDKfZKfDZK 19 28.42 3407 0.036102142 z340 2 +++z+ 5 3 ++z+++z++z+z+++z++++z++++z++++zz+ 33 8.18 1291979 0.03715076 z340 2 BBz 3 4 BBzzzzBzBBBzBBzBBzBBz 21 18.29 1291979 0.03798901 z340 4 RDYR4 5 3 RDYR4RDYR4RDYR4R444RYD 22 24.55 3407 0.04021133 z340 2 OK 2 6 OKOKOKOKOKOKOOOOK 17 50.82 1291979 0.040407002 z340 3 +++++++q++++A+ 14 2 +++++++q++++A++++++++q++++A+ 28 12.00 63860 0.04051049 z340 4 FKO< 4 3 O<KOKFFOFKO<FKO<FKO<FFFKO<FOF<OOK 33 13.09 3407 0.041385382 z340 4 lOKz 4 3 lOKzlOKzlOKzOzKzlOKOlzlzKOlzOOzOK 33 13.09 3407 0.041385382 z340 3 KO< 3 4 O<KOKOKO<KO<KO<KO<O<OOK 23 25.04 63860 0.04390855 z340 3 lV| 3 4 lV|lV|lV|lV|l||lVV|l||| 23 25.04 63860 0.04390855 z340 4 ++Z++++&+;++ 12 2 ++Z++++&+;++++Z++++&+;++Z+++++Z;+ 33 11.64 3407 0.051071323 z340 4 +++++&+;f+++ 12 2 +f+++++&+;f++++++++&+;f+++f++++;+ 33 11.64 3407 0.051071323 z340 4 +B+|B(+ 7 2 |+B(B+(+++|+(+|(++++B++B+|B|+B+|B(++B+|B(++B|++(|BB|+ 53 4.23 3407 0.05782213 z340 4 ++|c2c+ 7 2 |2+c+++2+|+2+2c|2++++2c+++|2c|++|c2c+++|c2c++|++c|c|+ 53 4.23 3407 0.05782213 z340 4 +B+5Bc5 7 2 +BBc++++5+5+c++++Bc++B+5Bc5+B+5Bc5c++B5+cBc++B++cBBc+ 53 4.23 3407 0.05782213 z340 3 -O< 3 4 O<OO-O<-O<-O<-O<O<O-O 21 27.43 63860 0.059818354 z340 3 UO< 3 4 O<UOOUO<UO<UO<UO<O<OO 21 27.43 63860 0.059818354 z340 3 JMc 3 4 cMJMcJMcJMcJMcccMcccM 21 27.43 63860 0.059818354 z340 3 ++7+++++X++++ 13 2 ++7+++++X++++++7+++++X+++++7+ 29 10.76 63860 0.06244911 z340 4 KOFy 4 3 OKyOKFFOFKOFyKOFyKOFyFFyKOFOFOOK 32 13.50 3407 0.06281186 z340 4 ^OKz 4 3 ^OKz^OKz^OKzOzKz^OKOz^zKO^zOOzOK 32 13.50 3407 0.06281186 z340 3 lVM 3 4 lVMlVMlVMlVMlMlVVMlM 20 28.80 63860 0.06291889 z340 3 *BBtB 5 3 B*B*t*BBtB*BBtB*BBtBB* 22 18.41 63860 0.065925464 z340 3 BlBz 4 3 lBBzlzlzzBzlBBlBzBlBzBlBzBBz 28 11.57 63860 0.067601
Can we conclude anything from these unusual patterns?
Can we conclude anything from these unusual patterns?
In the 408, your analysis found pattern "Uk+PUkPUk+PUkP+" in "PUk+PUkPUk+PUkP+Uk+PUkPUk+PUkP+U+P+PUk". "PU9k" is a real cycle in the 408 which then coincides with a symbol from another cycle. Seems like, pattern "123123123" in "123123123123123123".
I’m really not sure, your results seems to gravitate towards the symbols which have the most repeats. Also, in the 340, the "+" symbol spreads out quite evenly throughout the cipher so it has allot of potential to get caught up with other symbols in so many ways.
I wrote a quick and dirty palindromic sequence search. Smokie, some initial results are below from running it for L=4 (only considering 4 symbols at a time) on your 2nd palindromic cycles cipher. Do any of them look right?
31.0: 24 23 23 24 24 23 45 45 23 24 24 23 45 23 24 45 24 23 45 23 24 24 23 45 45 23 24 24 23 23 24 29.121212: 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 28.125: 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 28.125: 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 25.037037: 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 25.037037: 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 25.0: 24 22 24 24 45 22 45 24 24 22 45 24 45 24 45 22 24 24 45 22 45 24 24 22 24 25.0: 23 22 23 23 45 22 45 23 23 22 45 23 45 23 45 22 23 23 45 22 45 23 23 22 23 24.142857: 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 24.038462: 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24.038462: 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 24.038462: 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 24.038462: 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 23.148148: 23 24 24 23 23 24 24 23 23 24 24 23 60 23 24 24 23 23 24 24 23 23 24 24 23 23.148148: 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 22.153847: 12 13 1 13 12 12 13 1 13 12 12 13 13 12 12 13 1 13 12 12 13 1 13 12 22.0: 36 52 51 36 51 52 52 51 36 51 52 52 51 36 51 52 52 51 36 51 52 36 22.0: 24 23 23 24 24 23 42 23 24 24 23 23 24 24 23 42 23 24 24 23 23 24 22.0: 13 12 12 13 27 13 12 12 13 13 12 12 13 13 12 12 13 27 13 12 12 13 21.16: 24 24 45 44 45 24 24 44 45 24 44 45 44 24 45 44 24 24 45 44 45 24 24 21.0: 53 52 51 51 52 53 52 51 51 52 53 52 51 51 52 53 52 51 51 52 53 21.0: 31 30 29 29 30 31 30 29 29 30 31 30 29 29 30 31 30 29 29 30 31 21.0: 30 29 22 29 30 30 29 29 22 30 22 30 22 29 29 30 30 29 22 29 30 21.0: 24 23 23 24 24 23 23 24 24 23 43 23 24 24 23 23 24 24 23 23 24 21.0: 24 22 24 24 4 22 24 24 22 24 4 24 22 24 24 22 4 24 24 22 24 21.0: 24 22 24 24 34 22 24 24 22 24 34 24 22 24 24 22 34 24 24 22 24 21.0: 13 54 13 14 14 13 13 14 14 13 54 13 14 14 13 13 14 14 13 54 13 21.0: 11 14 15 14 11 14 15 14 11 14 15 14 11 14 15 14 11 14 15 14 11 20.828571: 23 12 13 23 23 13 23 12 12 13 23 13 12 23 12 13 23 13 12 12 23 13 23 23 13 12 23 20.346153: 23 23 24 24 23 23 24 24 23 23 24 61 24 23 23 24 24 23 23 24 24 23 23 20.166666: 23 25 23 23 25 23 53 23 25 53 23 23 53 25 23 53 23 25 23 23 25 23 20.045454: 11 13 15 13 11 13 15 13 11 13 15 13 11 13 15 13 11 13 15 13 11 20.045454: 11 12 15 12 11 12 15 12 11 12 15 12 11 12 15 12 11 12 15 12 11 20.0: 13 13 14 14 13 42 13 14 14 13 13 14 14 13 42 13 14 14 13 13 19.173914: 50 51 52 52 51 50 51 52 52 51 50 51 52 52 51 50 51 52 52 51 50 19.173914: 28 29 30 30 29 28 29 30 30 29 28 29 30 30 29 28 29 30 30 29 28 19.173914: 24 25 24 8 24 25 24 24 25 24 8 24 25 24 24 25 24 8 24 25 24 19.173914: 24 25 24 44 24 25 24 44 24 44 25 44 24 44 24 25 24 44 24 25 24 19.047619: 11 13 1 13 11 13 1 13 11 13 13 11 13 1 13 11 13 1 13 11 19.047619: 11 12 7 12 11 12 7 12 11 12 12 11 12 7 12 11 12 7 12 11 19.047619: 11 12 1 12 11 12 1 12 11 12 12 11 12 1 12 11 12 1 12 11 19.0: 30 29 1 29 30 30 29 29 30 1 30 29 29 30 30 29 1 29 30 19.0: 24 28 22 24 24 28 22 24 24 22 24 24 22 28 24 24 22 28 24 19.0: 21 51 21 50 51 21 51 50 51 21 51 50 51 21 51 50 21 51 21 19.0: 13 13 14 14 13 13 14 14 13 26 13 14 14 13 13 14 14 13 13 18.181818: 11 12 31 12 11 12 31 12 11 12 12 11 12 31 12 11 12 31 12 11 18.05: 24 25 24 24 25 24 24 25 24 60 24 25 24 24 25 24 24 25 24 18.05: 23 25 23 23 25 23 23 25 23 60 23 25 23 23 25 23 23 25 23 18.05: 13 1 15 13 13 15 1 13 13 15 13 13 1 15 13 13 15 1 13 18.05: 12 1 15 12 12 15 1 12 12 15 12 12 1 15 12 12 15 1 12 18.0: 52 51 51 49 52 52 51 51 52 52 51 51 52 52 49 51 51 52 18.0: 36 35 20 35 36 20 20 36 35 35 36 20 20 36 35 20 35 36 18.0: 30 29 29 30 30 29 29 42 30 30 42 29 29 30 30 29 29 30 18.0: 13 36 13 14 14 13 36 13 14 14 13 36 13 14 14 13 36 13 18.0: 13 12 12 13 57 13 12 12 13 13 12 12 13 57 13 12 12 13 18.0: 13 12 12 13 13 12 4 12 13 13 12 4 12 13 13 12 12 13 18.0: 11 39 40 11 40 39 39 40 11 11 40 39 39 40 11 40 39 11 17.64: 23 22 23 21 23 22 21 23 21 23 22 23 21 23 21 22 23 21 23 22 23 17.64: 14 24 14 24 24 14 24 14 24 14 24 14 24 14 24 14 24 24 14 24 14 17.64: 14 23 23 14 23 14 23 38 14 23 14 23 14 38 23 14 23 14 23 23 14 17.285715: 24 24 23 23 24 24 23 23 24 24 23 23 24 24 23 23 24 24 23 23 24 24 17.190475: 42 51 52 52 51 51 52 52 51 42 51 52 52 51 51 52 52 51 42 17.190475: 30 31 30 45 45 30 31 30 45 45 45 30 31 30 45 45 30 31 30 17.190475: 23 22 23 23 22 23 23 22 23 61 23 22 23 23 22 23 23 22 23 17.190475: 22 29 24 29 24 29 22 24 24 22 24 24 22 29 24 29 24 29 22 17.052631: 39 40 3 3 40 39 3 39 40 40 39 3 39 40 3 3 40 39 17.052631: 11 40 3 11 3 40 3 40 11 11 40 3 40 3 11 3 40 11 17.052631: 11 39 3 11 3 39 3 39 11 11 39 3 39 3 11 3 39 11 17.0: 46 32 33 32 33 46 32 33 32 33 32 46 33 32 33 32 46 17.0: 44 53 44 50 53 44 50 44 53 44 50 44 53 50 44 53 44 17.0: 44 45 44 45 49 44 45 44 45 44 45 44 49 45 44 45 44 17.0: 44 15 45 44 45 15 44 45 44 45 44 15 45 44 45 15 44 17.0: 39 40 48 40 39 48 39 40 48 40 39 48 39 40 48 40 39 17.0: 36 52 4 36 52 52 36 52 4 52 36 52 52 36 4 52 36 17.0: 31 8 29 29 31 29 29 8 31 8 29 29 31 29 29 8 31 17.0: 30 29 29 30 30 29 29 30 43 30 29 29 30 30 29 29 30 17.0: 30 28 22 30 30 28 22 30 22 30 22 28 30 30 22 28 30 17.0: 29 28 22 29 29 28 29 22 22 22 29 28 29 29 22 28 29 17.0: 24 28 1 24 24 28 24 24 1 24 24 28 24 24 1 28 24 17.0: 24 1 24 25 24 24 25 24 1 24 25 24 24 25 24 1 24 17.0: 23 22 23 27 23 22 23 23 22 23 23 22 23 27 23 22 23 17.0: 21 51 21 51 49 21 51 51 21 51 51 21 49 51 21 51 21 17.0: 21 20 21 50 20 21 20 50 21 50 20 21 20 50 21 20 21 17.0: 13 54 13 15 13 13 15 13 54 13 15 13 13 15 13 54 13 17.0: 13 12 12 13 13 12 12 13 43 13 12 12 13 13 12 12 13 17.0: 13 11 13 27 13 11 13 13 11 13 13 11 13 27 13 11 13 17.0: 13 11 13 13 11 42 13 13 11 13 13 42 11 13 13 11 13 17.0: 12 11 12 27 12 11 12 12 11 12 12 11 12 27 12 11 12 16.961538: 14 23 23 14 58 23 14 23 14 23 14 23 14 23 14 23 58 14 23 23 14 16.666666: 13 29 29 13 12 29 12 13 13 12 12 13 13 12 29 12 13 29 29 13 16.40909: 8 51 52 52 51 51 52 52 51 8 51 52 52 51 51 52 52 51 8 16.40909: 5 51 52 52 51 51 52 52 51 5 51 52 52 51 51 52 52 51 5 16.40909: 24 24 45 45 31 24 24 45 24 45 24 45 24 24 31 45 45 24 24 16.40909: 24 24 23 23 24 24 23 23 24 26 24 23 23 24 24 23 23 24 24 16.40909: 14 24 24 14 24 49 14 24 14 24 14 24 14 49 24 14 24 24 14 16.333334: 23 13 23 23 13 23 4 13 23 13 23 13 23 13 4 23 13 23 23 13 23 16.2: 39 2 3 3 2 39 2 3 39 39 3 2 39 2 3 3 2 39 16.2: 29 24 29 25 24 29 24 25 24 24 25 24 29 24 25 29 24 29 16.2: 28 29 24 29 24 28 29 24 24 24 24 29 28 24 29 24 29 28
The first number is a crude score based on sequence length and how much of the full sequence it covers. The rest of each line indicates the palindromic sequence found. Since the algorithm only checks if the string is palindromic, it tends to also find strings with long patterns that repeat infrequently. I need to refine it to score those properly so spurious coincidences aren’t included with higher quality sequences.
I wrote a quick and dirty palindromic sequence search. Smokie, some initial results are below from running it for L=4 (only considering 4 symbols at a time) on your 2nd palindromic cycles cipher. Do any of them look right?
31.0: 24 23 23 24 24 23 45 45 23 24 24 23 45 23 24 45 24 23 45 23 24 24 23 45 45 23 24 24 23 23 24 29.121212: 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 23 24 24 23 22 28.125: 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 23 24 25 24 23 28.125: 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 12 13 14 14 13 12 25.037037: 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 13 14 14 13 11 25.037037: 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 12 14 14 12 11 25.0: 24 22 24 24 45 22 45 24 24 22 45 24 45 24 45 22 24 24 45 22 45 24 24 22 24 25.0: 23 22 23 23 45 22 45 23 23 22 45 23 45 23 45 22 23 23 45 22 45 23 23 22 23 24.142857: 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 12 13 13 12 11 24.038462: 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24 25 24 22 24.038462: 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 23 25 23 22 24.038462: 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 13 14 15 14 13 24.038462: 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 12 14 15 14 12 23.148148: 23 24 24 23 23 24 24 23 23 24 24 23 60 23 24 24 23 23 24 24 23 23 24 24 23 23.148148: 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 12 13 15 13 12 22.153847: 12 13 1 13 12 12 13 1 13 12 12 13 13 12 12 13 1 13 12 12 13 1 13 12 22.0: 36 52 51 36 51 52 52 51 36 51 52 52 51 36 51 52 52 51 36 51 52 36 22.0: 24 23 23 24 24 23 42 23 24 24 23 23 24 24 23 42 23 24 24 23 23 24 22.0: 13 12 12 13 27 13 12 12 13 13 12 12 13 13 12 12 13 27 13 12 12 13 21.16: 24 24 45 44 45 24 24 44 45 24 44 45 44 24 45 44 24 24 45 44 45 24 24 21.0: 53 52 51 51 52 53 52 51 51 52 53 52 51 51 52 53 52 51 51 52 53 21.0: 31 30 29 29 30 31 30 29 29 30 31 30 29 29 30 31 30 29 29 30 31 21.0: 30 29 22 29 30 30 29 29 22 30 22 30 22 29 29 30 30 29 22 29 30 21.0: 24 23 23 24 24 23 23 24 24 23 43 23 24 24 23 23 24 24 23 23 24 21.0: 24 22 24 24 4 22 24 24 22 24 4 24 22 24 24 22 4 24 24 22 24 21.0: 24 22 24 24 34 22 24 24 22 24 34 24 22 24 24 22 34 24 24 22 24 21.0: 13 54 13 14 14 13 13 14 14 13 54 13 14 14 13 13 14 14 13 54 13 21.0: 11 14 15 14 11 14 15 14 11 14 15 14 11 14 15 14 11 14 15 14 11 20.828571: 23 12 13 23 23 13 23 12 12 13 23 13 12 23 12 13 23 13 12 12 23 13 23 23 13 12 23 20.346153: 23 23 24 24 23 23 24 24 23 23 24 61 24 23 23 24 24 23 23 24 24 23 23 20.166666: 23 25 23 23 25 23 53 23 25 53 23 23 53 25 23 53 23 25 23 23 25 23 20.045454: 11 13 15 13 11 13 15 13 11 13 15 13 11 13 15 13 11 13 15 13 11 20.045454: 11 12 15 12 11 12 15 12 11 12 15 12 11 12 15 12 11 12 15 12 11 20.0: 13 13 14 14 13 42 13 14 14 13 13 14 14 13 42 13 14 14 13 13 19.173914: 50 51 52 52 51 50 51 52 52 51 50 51 52 52 51 50 51 52 52 51 50 19.173914: 28 29 30 30 29 28 29 30 30 29 28 29 30 30 29 28 29 30 30 29 28 19.173914: 24 25 24 8 24 25 24 24 25 24 8 24 25 24 24 25 24 8 24 25 24 19.173914: 24 25 24 44 24 25 24 44 24 44 25 44 24 44 24 25 24 44 24 25 24 19.047619: 11 13 1 13 11 13 1 13 11 13 13 11 13 1 13 11 13 1 13 11 19.047619: 11 12 7 12 11 12 7 12 11 12 12 11 12 7 12 11 12 7 12 11 19.047619: 11 12 1 12 11 12 1 12 11 12 12 11 12 1 12 11 12 1 12 11 19.0: 30 29 1 29 30 30 29 29 30 1 30 29 29 30 30 29 1 29 30 19.0: 24 28 22 24 24 28 22 24 24 22 24 24 22 28 24 24 22 28 24 19.0: 21 51 21 50 51 21 51 50 51 21 51 50 51 21 51 50 21 51 21 19.0: 13 13 14 14 13 13 14 14 13 26 13 14 14 13 13 14 14 13 13 18.181818: 11 12 31 12 11 12 31 12 11 12 12 11 12 31 12 11 12 31 12 11 18.05: 24 25 24 24 25 24 24 25 24 60 24 25 24 24 25 24 24 25 24 18.05: 23 25 23 23 25 23 23 25 23 60 23 25 23 23 25 23 23 25 23 18.05: 13 1 15 13 13 15 1 13 13 15 13 13 1 15 13 13 15 1 13 18.05: 12 1 15 12 12 15 1 12 12 15 12 12 1 15 12 12 15 1 12 18.0: 52 51 51 49 52 52 51 51 52 52 51 51 52 52 49 51 51 52 18.0: 36 35 20 35 36 20 20 36 35 35 36 20 20 36 35 20 35 36 18.0: 30 29 29 30 30 29 29 42 30 30 42 29 29 30 30 29 29 30 18.0: 13 36 13 14 14 13 36 13 14 14 13 36 13 14 14 13 36 13 18.0: 13 12 12 13 57 13 12 12 13 13 12 12 13 57 13 12 12 13 18.0: 13 12 12 13 13 12 4 12 13 13 12 4 12 13 13 12 12 13 18.0: 11 39 40 11 40 39 39 40 11 11 40 39 39 40 11 40 39 11 17.64: 23 22 23 21 23 22 21 23 21 23 22 23 21 23 21 22 23 21 23 22 23 17.64: 14 24 14 24 24 14 24 14 24 14 24 14 24 14 24 14 24 24 14 24 14 17.64: 14 23 23 14 23 14 23 38 14 23 14 23 14 38 23 14 23 14 23 23 14 17.285715: 24 24 23 23 24 24 23 23 24 24 23 23 24 24 23 23 24 24 23 23 24 24 17.190475: 42 51 52 52 51 51 52 52 51 42 51 52 52 51 51 52 52 51 42 17.190475: 30 31 30 45 45 30 31 30 45 45 45 30 31 30 45 45 30 31 30 17.190475: 23 22 23 23 22 23 23 22 23 61 23 22 23 23 22 23 23 22 23 17.190475: 22 29 24 29 24 29 22 24 24 22 24 24 22 29 24 29 24 29 22 17.052631: 39 40 3 3 40 39 3 39 40 40 39 3 39 40 3 3 40 39 17.052631: 11 40 3 11 3 40 3 40 11 11 40 3 40 3 11 3 40 11 17.052631: 11 39 3 11 3 39 3 39 11 11 39 3 39 3 11 3 39 11 17.0: 46 32 33 32 33 46 32 33 32 33 32 46 33 32 33 32 46 17.0: 44 53 44 50 53 44 50 44 53 44 50 44 53 50 44 53 44 17.0: 44 45 44 45 49 44 45 44 45 44 45 44 49 45 44 45 44 17.0: 44 15 45 44 45 15 44 45 44 45 44 15 45 44 45 15 44 17.0: 39 40 48 40 39 48 39 40 48 40 39 48 39 40 48 40 39 17.0: 36 52 4 36 52 52 36 52 4 52 36 52 52 36 4 52 36 17.0: 31 8 29 29 31 29 29 8 31 8 29 29 31 29 29 8 31 17.0: 30 29 29 30 30 29 29 30 43 30 29 29 30 30 29 29 30 17.0: 30 28 22 30 30 28 22 30 22 30 22 28 30 30 22 28 30 17.0: 29 28 22 29 29 28 29 22 22 22 29 28 29 29 22 28 29 17.0: 24 28 1 24 24 28 24 24 1 24 24 28 24 24 1 28 24 17.0: 24 1 24 25 24 24 25 24 1 24 25 24 24 25 24 1 24 17.0: 23 22 23 27 23 22 23 23 22 23 23 22 23 27 23 22 23 17.0: 21 51 21 51 49 21 51 51 21 51 51 21 49 51 21 51 21 17.0: 21 20 21 50 20 21 20 50 21 50 20 21 20 50 21 20 21 17.0: 13 54 13 15 13 13 15 13 54 13 15 13 13 15 13 54 13 17.0: 13 12 12 13 13 12 12 13 43 13 12 12 13 13 12 12 13 17.0: 13 11 13 27 13 11 13 13 11 13 13 11 13 27 13 11 13 17.0: 13 11 13 13 11 42 13 13 11 13 13 42 11 13 13 11 13 17.0: 12 11 12 27 12 11 12 12 11 12 12 11 12 27 12 11 12 16.961538: 14 23 23 14 58 23 14 23 14 23 14 23 14 23 14 23 58 14 23 23 14 16.666666: 13 29 29 13 12 29 12 13 13 12 12 13 13 12 29 12 13 29 29 13 16.40909: 8 51 52 52 51 51 52 52 51 8 51 52 52 51 51 52 52 51 8 16.40909: 5 51 52 52 51 51 52 52 51 5 51 52 52 51 51 52 52 51 5 16.40909: 24 24 45 45 31 24 24 45 24 45 24 45 24 24 31 45 45 24 24 16.40909: 24 24 23 23 24 24 23 23 24 26 24 23 23 24 24 23 23 24 24 16.40909: 14 24 24 14 24 49 14 24 14 24 14 24 14 49 24 14 24 24 14 16.333334: 23 13 23 23 13 23 4 13 23 13 23 13 23 13 4 23 13 23 23 13 23 16.2: 39 2 3 3 2 39 2 3 39 39 3 2 39 2 3 3 2 39 16.2: 29 24 29 25 24 29 24 25 24 24 25 24 29 24 25 29 24 29 16.2: 28 29 24 29 24 28 29 24 24 24 24 29 28 24 29 24 29 28The first number is a crude score based on sequence length and how much of the full sequence it covers. The rest of each line indicates the palindromic sequence found. Since the algorithm only checks if the string is palindromic, it tends to also find strings with long patterns that repeat infrequently. I need to refine it to score those properly so spurious coincidences aren’t included with higher quality sequences.
Doranchak, most of the highest scoring palindromic cycles are true cycles. But I find it interesting that many of the lower palindromic cycles are false. Here is the key, which is pretty simple. If you see something like 1 2 3 4 3 2 1, then those symbols all probably map to the same plaintext. But 1 2 3 15 3 2 1 2 3 15 3 2 would not because the numbers are not next to each other on the number line.
A 1 2 3 4 3 2
B 5 6
C 7 8
D 9 10
E 11 12 13 14 15 14 13 12
F 16 17
G 18 19
H 20 21
I 22 23 24 25 24 23
J
K 26 27
L 28 29 30 31 30 29
M 32 33
N 34 35 36 37 36 35
O 38 39 40 41 40 39
P 42 43
Q
R 44 45
S 46 47 48 49 48 47
T 50 51 52 53 52 51
U 54 55
V 56 57
W 58 59
X 60
Y 61 62
Z
Thanks for your work. It is greatly appreciated. Soon I would like to add a link to your spreadsheet to my table of contents.
I have been thinking a lot about this one, how to interpret it and what to say. I need to take a closer look and mull it over.
+F+FF+++++F++F+
+F+FF+++++F++F+
I made some changes to my palindrome finding algorithm and it found some palindromic cycles in Z340 for L=4. Columns are: score, palindromic sequence, sequence length, full string length, full string:
14.769231 /p(;(p/p(;(p/ 13 17 pp((ppp/p(;(p/p(;(p/(pp; 14.769231 /p(X(p/p(X(p/ 13 16 pp((ppp/p(X(p/p(X(p/(pp 14.769231 ;N-7-N;N-7-N; 13 13 N7-;N-7-N;N-7-N; 14.769231 .cU7Uc.cU7Uc. 13 24 .cU7Uc.cU7Uc.c.cUc..cc7c 14.769231 /pK;Kp/pK;Kp/ 13 17 ppKpppK/pK;Kp/pK;Kp/ppK; 14.769231 /pKXKp/pKXKp/ 13 16 ppKpppK/pKXKp/pKXKp/ppK 14.769231 /pKZKp/pKZKp/ 13 17 ppKZpppK/pKZKp/pKZKp/ppZK 14.769231 NcU7UcNcU7UcN 13 23 NcU7UcNcU7UcNcNcUccc7cN
And for L=3:
24.923077 ^c9c^c9c^c9c^ 13 16 ^c^9^c9c^c9c^c9c^ccc 24.923077 DKZKDKZKDKZKD 13 15 DKZKDKZKDKZKDZK 12.0 y|D|yy|D|y 10 17 |Dy|D|yy|D|y|y|||D| 12.0 y5D5yy5D5y 10 15 Dy5D5yy5D5y55y5D 12.0 pp(.(pppp(.(pp 14 24 pp(.(pppp(.(pp.(..(p.(pp 12.0 pp(%(pppp(%(pp 14 20 pp(%(pppp(%(pp((p(pp 12.0 pp#f#pppp#f#pp 14 20 pp#f#pppp#f#pp#fpfpp 12.0 pp#.#pppp#.#pp 14 22 pp#.#pppp#.#pp.#..p.pp 12.0 pp#%#pppp#%#pp 14 18 pp#%#pppp#%#pp#ppp 12.0 pl;lppl;lp 10 14 plppplppl;lppl;lplpp; 12.0 pl6lppl6lp 10 14 plppplppl6lppl6lp6lpp 12.0 pKfKppKfKp 10 14 ppKfpppKpKfKppKfKpfppK 12.0 pKZKppKZKp 10 14 ppKZpppKpKZKppKZKpppZK 12.0 pKXKppKXKp 10 13 ppKpppKpKXKppKXKpppK 12.0 pK;KppK;Kp 10 14 ppKpppKpK;KppK;KpppK; 12.0 pK6KppK6Kp 10 14 ppKpppKpK6KppK6Kp6ppK 12.0 p(X(pp(X(p 10 13 pp((pppp(X(pp(X(p(pp 12.0 p(;(pp(;(p 10 14 pp((pppp(;(pp(;(p(pp; 12.0 lptpllptpl 10 17 plppplptpllptplltplptp 12.0 lp/pllp/pl 10 16 plppplp/pllp/pllpl/pp 12.0 lLfLllLfLl 10 17 lLfLllLfLlllffLlL 12.0 lLYLllLYLl 10 17 lLYLllLYLlYllLlLY 12.0 lLNLllLNLl 10 18 lLNLllLNLllNlNLlLN 12.0 lG.GllG.Gl 10 19 lG.GllG.Gll.lG...Gl 12.0 l(U(ll(U(l 10 19 l(U(ll(U(lUUl(lU(l( 12.0 l(.(ll(.(l 10 20 l(.(ll(.(ll.(l..(.l( 12.0 l(%(ll(%(l 10 16 l(%(ll(%(ll(l(l( 12.0 l#f#ll#f#l 10 16 l#f#ll#f#ll#lffl 12.0 l#U#ll#U#l 10 17 l#U#ll#U#lUUl#lUl 12.0 l#.#ll#.#l 10 18 l#.#ll#.#ll.#l...l 12.0 l#%#ll#%#l 10 14 l#%#ll#%#ll#ll 12.0 dz_zddz_zd 10 17 dz_zddz_zdzzzzd_z 12.0 dzJzddzJzd 10 18 dzJzddzJzdzJJzzzdz 12.0 d(c(dd(c(d 10 22 d(c(dd(c(dccc(cc(cc(dc 12.0 d(U(dd(U(d 10 17 d(U(dd(U(dUU(U((d 12.0 d(.(dd(.(d 10 18 d(.(dd(.(d.(..(.(d 12.0 d(%(dd(%(d 10 14 d(%(dd(%(d(((d 12.0 d#f#dd#f#d 10 14 d#f#dd#f#d#ffd 12.0 d#c#dd#c#d 10 20 d#c#dd#c#dcc#cccccdc 12.0 d#U#dd#U#d 10 15 d#U#dd#U#dUU#Ud 12.0 d#.#dd#.#d 10 16 d#.#dd#.#d.#...d 12.0 d#%#dd#%#d 10 12 d#%#dd#%#d#d 12.0 cU7UccU7Uc 10 18 cU7UccU7UcccUccc7c 12.0 cKtKccKtKc 10 20 KcKtKccKtKccctcKcctcK 12.0 cKDKccKDKc 10 19 DKcKDKccKDKccccKcccDK 12.0 cK/KccK/Kc 10 19 KcK/KccK/KccccKcc/cK 12.0 ^ptp^^ptp^ 10 16 p^ppp^ptp^^ptp^tp^ptp 12.0 ^p/p^^p/p^ 10 15 p^ppp^p/p^^p/p^p^/pp 12.0 ^LfL^^LfL^ 10 16 ^LfL^^LfL^^f^fLL 12.0 ^LYL^^LYL^ 10 16 ^LYL^^LYL^Y^^LLY 12.0 ^LNL^^LNL^ 10 17 ^LNL^^LNL^NN^^LLN 12.0 ^G.G^^G.G^ 10 18 ^G.G^^G.G^.G^..^.G 12.0 ^(.(^^(.(^ 10 19 ^(.(^^(.(^.(^..(^.( 12.0 ^#f#^^#f#^ 10 15 ^#f#^^#f#^#^f^f 12.0 ^#.#^^#.#^ 10 17 ^#.#^^#.#^.#^..^. 12.0 ^#%#^^#%#^ 10 13 ^#%#^^#%#^#^^ 12.0 YfXfYYfXfY 10 10 YfXfYYfXfY 12.0 Yf>fYYf>fY 10 11 >Yf>fYYf>fY> 12.0 Yf:fYYf:fY 10 10 Yf:fYYf:fY 12.0 Yf3fYYf3fY 10 10 Yf3fYYf3fY 12.0 VptpVVptpV 10 16 pVpppVptpVVptpVtVpptp 12.0 Vp/pVVp/pV 10 15 pVpppVp/pVVp/pVVp/pp 12.0 VLfLVVLfLV 10 16 VLfLVVLfLVfVVfLL 12.0 VLYLVVLYLV 10 16 VLYLVVLYLVYVVLLY 12.0 VLNLVVLNLV 10 17 VLNLVVLNLVNNVVLLN 12.0 U2f2UU2f2U 10 12 2fU222U2f2UU2f2Uf2 12.0 U2#2UU2#2U 10 11 2#U#22#2U2#2UU2#2U2 12.0 TfXfTTfXfT 10 11 TfXfTTfXfTT 12.0 TfCfTTfCfT 10 14 TfCfTTfCfTCCTC 12.0 Tf>fTTf>fT 10 12 >Tf>fTTf>fTT> 12.0 Tf:fTTf:fT 10 11 Tf:fTTf:fTT 12.0 Tf3fTTf3fT 10 11 Tf3fTTf3fTT 12.0 TN;NTTN;NT 10 13 TN;NTTN;NTTN; 12.0 T9X9TT9X9T 10 11 T9X9TT9X9TT 12.0 T9;9TT9;9T 10 12 T9;9TT9;9TT; 12.0 ROfORROfOR 10 22 ROfORROfORORORRfOfROOO 12.0 ROcORROcOR 10 28 ROcORROcORcOROcRcRccORccOOcO 12.0 ROUORROUOR 10 23 ROUORROUORUOURORRUOROOO 12.0 ROJORROJOR 10 22 ROJORROJORJORORJROROOO 12.0 RODORRODOR 10 22 RODORRODORORDORROROODO 12.0 RO.ORRO.OR 10 24 RO.ORRO.OROROR.R..O.ROOO 12.0 RO%ORRO%OR 10 20 RO%ORRO%ORORORROROOO 12.0 RLfLRRLfLR 10 18 RLfLRRLfLRRRRffRLL 12.0 RLYLRRLYLR 10 18 RLYLRRLYLRRYRRRLLY 12.0 RLNLRRLNLR 10 19 RLNLRRLNLRRRNRNRLLN 12.0 RG.GRRG.GR 10 20 RG.GRRG.GRRR.RG...GR 12.0 RFzFRRFzFR 10 17 RzRzFRFFzzRFzFRRFzFRFzRFzFz 12.0 RF6FRRF6FR 10 15 RRFRFFRF6FRRF6FRFR6FF 12.0 R(c(RR(c(R 10 25 R(c(RR(c(RcRcRc(Rcc(Rcc(c 12.0 R(U(RR(U(R 10 20 R(U(RR(U(RUURR(RU(R( 12.0 R(.(RR(.(R 10 21 R(.(RR(.(RRR.(R..(.R( 12.0 R(%(RR(%(R 10 17 R(%(RR(%(RRR(R(R( 12.0 R#f#RR#f#R 10 17 R#f#RR#f#RRR#RffR 12.0 R#c#RR#c#R 10 23 R#c#RR#c#RcRcR#cRccRccc 12.0 R#U#RR#U#R 10 18 R#U#RR#U#RUURR#RUR 12.0 R#.#RR#.#R 10 19 R#.#RR#.#RRR.#R...R 12.0 R#%#RR#%#R 10 15 R#%#RR#%#RRR#RR 12.0 Np/pNNp/pN 10 11 pNpppp/pNp/pNNp/pNp 12.0 N2E2NN2E2N 10 10 E2N2222N2E2NN2E2N 12.0 N-7-NN-7-N 10 10 N7-N-7-NN-7-N
But many similar sequences are found for Z408 L=4:
16.0 PM!MP\PM!MP 14 23 PP!MPMPM!MP\PM!MPPMP!!PPM 16.0 G@^kk^@GG@^kk^@G 16 27 kG@^kk^@GG@^kk^@Gkk^Gk@^GG@k 16.0 +PM!MP++PM!MP+ 14 25 P+P!MPM+PM!MP++PM!MP+PMP++!!P+PM 15.058824 P@^kPk^@P@^kPk^@P 17 30 PkP@^kPk^@P@^kPk^@PkPkP^kP@^P@Pk 15.058824 OG@^O^@GOG@^O^@GO 17 26 OG@^O^@GOG@^O^@GO^G@O^GOG@ 14.769231 TPMKMPTPMKMPT 13 23 PPKMTPMKTPMKMPTPMKMPTPMPTKTPTPM 14.769231 TPM!MPTPM!MPT 13 24 PP!MTPMTPM!MPTPM!MPTPMPTT!!PTPM 14.769231 OPMKMPOPMKMPO 13 22 POPKMPOMKOPMKMPOPMKMPOPMPOKPOPM 14.769231 OPM!MPOPM!MPO 13 23 POP!MPOMOPM!MPOPM!MPOPMPO!!POPM 14.769231 K8M(M8K8M(M8K 13 15 KM(M8K8(8MK8M(M8K8M(M8K8M 14.769231 Gr9(9rGr9(9rG 13 23 9G9(9rG9(Gr9(9rGr9(9rG999G99Grr9 14.769231 /r9(9r/r9(9r/ 13 21 9//9(/9r9(/r9(9r/r9(9r/99999rr9 14.769231 !8M(M8!8M(M8! 13 16 !M(M88(8M!8M(M8!8M(M8!!8M 8.533334 pHELpHELEHpLEHp 15 31 pHELpHELEHpLEHpLHLEHLpEpELHLEEH 8.533334 pH#LpH#L#HpL#Hp 15 32 pH#LpH#L#HpL#HpLHLHLp##p##LHL##H 8.533334 eDLpeDLpLDepLDe 15 28 peeDLpeDLpLDepLDeLLpeDpeeLDLee 8.533334 eDLZeDLZLDeZLDe 15 30 ZeeDLZeDLZLDeZLDeLLZeDZeZeLDLeeZ 8.533334 eDLWeDLWLDeWLDe 15 31 WeeDLWeDLWLDeWLDeLLWeDeWWeLDLeeWW 8.533334 eD9peD9p9Dep9De 15 32 9pe9eD9peD9p9Dep9De9p9eD9pe99e99Dee9 8.533334 eD9leD9l9Del9De 15 32 9e9eD9leD9l9Del9De9l9leD9e99e99Dee9 8.533334 eD9ZeD9Z9DeZ9De 15 34 9Ze9eD9ZeD9Z9DeZ9De9Z9eD9Ze99Ze99DeeZ9 8.533334 eD9WeD9W9DeW9De 15 35 9We9eD9WeD9W9DeW9De99WeD9eW99We99DeeW9W 8.533334 eD9OeD9O9DeO9De 15 33 9Oe9eD9OeD9O9DeO9De99OeD9e99Oe99DeeO9 8.533334 eD5peD5p5Dep5De 15 28 peeD5peD5p5Dep5De55peDpe5eDee5 8.533334 eD5ZeD5Z5DeZ5De 15 30 ZeeD5ZeD5Z5DeZ5De55ZeDZe5ZeDee5Z 8.533334 eD5WeD5W5DeW5De 15 31 WeeD5WeD5W5DeW5De55WeDeW5WeDee5WW 8.533334 eD5OeD5O5DeO5De 15 29 OeeD5OeD5O5DeO5De55OeDeO5eDee5O 8.533334 eD)peD)p)Dep)De 15 28 peeD)peD)p)Dep)De))peD)peeDee) 8.533334 eD)ZeD)Z)DeZ)De 15 30 ZeeD)ZeD)Z)DeZ)De))ZeD)ZeZeDeeZ) 8.533334 eD)OeD)O)DeO)De 15 29 OeeD)OeD)O)DeO)De))OeD)eOeDeeO) 8.533334 e9Lpe9LpL9epL9e 15 34 9pe9e9Lpe9LpL9epL9eL9Lp9e9pe99e9L9Lee9 8.533334 e9LZe9LZL9eZL9e 15 36 9Ze9e9LZe9LZL9eZL9eL9LZ9e9Ze99Ze9L9LeeZ9 8.533334 e9LWe9LWL9eWL9e 15 37 9We9e9LWe9LWL9eWL9eL9L9We9eW99We9L9LeeW9W 8.533334 dD6(dD6(6Dd(6Dd 15 21 6D(dD6(dD6(6Dd(6DdDdd666 8.533334 ZHELZHELEHZLEHZ 15 33 ZHELZHELEHZLEHZLHLEHLZEZZELHLZEEH 8.533334 ZH#LZH#L#HZL#HZ 15 34 ZH#LZH#L#HZL#HZLHLHLZ#Z##Z#LHL##ZH 8.533334 YD6(YD6(6DY(6DY 15 21 Y6YYYD(YD6(YD6(6DY(6DYYYD666 8.533334 OWr=OWr=rWO=rWO 15 23 O==WOrWOWr=OWr=rWO=rWOW=OrWrW= 8.533334 GD6OGD6O6DGO6DG 15 23 OG6DOGD6OGD6O6DGO6DGOGD6OG66 8.533334 GD6(GD6(6DG(6DG 15 21 G6D(GD6(GD6(6DG(6DGGD6G66 8.533334 EW+OEW+O+WEO+WE 15 17 OW+OEW+EOEW+EOW+EW+OEW+O+WEO+WEWE 8.533334 D9LpD9LpL9DpL9D 15 31 9p9D9LpD9LpL9DpL9DL9Lp9D9p999L9DL9 8.533334 D9LZD9LZL9DZL9D 15 33 9Z9D9LZD9LZL9DZL9DL9LZ9D9Z99Z9L9DLZ9 8.533334 D9LWD9LWL9DWL9D 15 34 9W9D9LWD9LWL9DWL9DL9L9WD9W99W9L9DLW9W 8.533334 @D6O@D6O6D@O6D@ 15 22 O6@DO@D6O@D6O6D@O6D@OD6O@66 8.533334 @D6(@D6(6D@(6D@ 15 20 6@D(@D6(@D6(6D@(6D@D6@66 8.533334 6W+O6W+O+W6O+W6 15 17 OW+6OW+6OW+6OW+6W+O6W+O+W6O+W6W6 8.533334 /^p(/^p(p^/(p^/ 15 17 //p^(/^p(/^p(p^/(p^/p^ 8.533334 /^ZK/^ZKZ^/KZ^/ 15 20 /Z/K^/^ZK/^ZKZ^/KZ^/Z^ZKZ 8.533334 /^W(/^W(W^/(W^/ 15 20 //W^(/^W(/^W(W^/(W^/W^WWW 8.533334 /^+(/^+(+^/(+^/ 15 19 //+^(/^+(/^+(+^/(+^/++^+ 8.533334 /D6(/D6(6D/(6D/ 15 19 //6D(/D6(/D6(6D/(6D/D666 8.0 eD9LeD9LL9DeL9De 16 35 9e9eD9LeD9LL9DeL9DeL9L9eD9e99e9L9DLee9 8.0 eD9EeD9EE9DeE9De 16 36 9e9eD9EeD9EE9DeE9DeE99eDE9e99eE99DeeE9E 8.0 eD5EeD5EE5DeE5De 16 32 eeD5EeD5EE5DeE5De5E5eDEe5eEDee5EE 8.0 eD)EeD)EE)DeE)De 16 32 eeD)EeD)EE)DeE)De)E)eD)EeeEDeeEE) 7.529412 BZ)rBZ)r)r)ZBr)ZB 17 25 ZBB)BZr)BBBZ)rBZ)r)r)ZBr)ZBBZBZrBr) 7.529412 #Z)r#Z)r)r)Z#r)Z# 17 26 Z)#Zr)##Z)r#Z)r)r)Z#r)Z##Z###Zrr)
And L=3:
24.923077 lINIlINIlINIl 13 20 INlINIlINIlINIlNlINIII 24.923077 l8K8l8K8l8K8l 13 17 Kl8K8l8K8l8K8ll8K8 24.923077 l8G8l8G8l8G8l 13 19 Gl8G8l8G8l8G8llG8GG8 24.923077 O8K8O8K8O8K8O 13 18 OKO8K8O8K8O8K8O8OKO8 24.923077 O8G8O8G8O8G8O 13 20 OGO8G8O8G8O8G8OG8OGOG8 24.923077 /EKE/EKE/EKE/ 13 17 //K/EKE/EKE/EKE/KEEE 24.923077 /E(E/E(E/E(E/ 13 16 //(/E(E/E(E/E(E/EEE 24.923077 (8K8(8K8(8K8( 13 16 K(8K8(8K8(8K8(8K8 24.923077 (8G8(8G8(8G8( 13 18 G(8G8(8G8(8G8(G8GG8 14.294118 OpDOpDOpDpODpODpO 17 19 OpDOpDOpDpODpODpODO 14.294118 Op6Op6Op6pO6pO6pO 17 21 Op6Op6Op6pO6pO6pO6O66 14.294118 )LH)LH)LHL)HL)HL) 17 23 H)LH)LH)LHL)HL)HL))LHLH) 12.0 tk(kttk(kt 10 14 kkt(k(tk(kttk(ktkttk 12.0 r9p9rr9p9r 10 19 9p99rp9pr9p9rr9p9r9p9999rr9 12.0 r9l9rr9l9r 10 19 999lr9lr9l9rr9l9rl99999rr9 12.0 r9Z9rr9Z9r 10 21 9Z99Zr9Zr9Z9rr9Z9r9Z99Z99Zrr9 12.0 r9(9rr9(9r 10 18 99(9r9(r9(9rr9(9r99999rr9 12.0 qc@cqqc@cq 10 16 @qqq@qqq@qcqqc@cqqc@cqqqc@qq 12.0 kVVkkVVk 10 15 kVkkVkkVVkkVVkVVVk 12.0 kVWVkkVWVk 10 18 kWVkkVWkWkVWVkkVWVkVWWVWVWk 12.0 kV+VkkV+Vk 10 17 kV+kkV+k+kV+VkkV+VkV++V+Vk 12.0 eN!NeeN!Ne 10 17 e!eNeN!NeeN!NeNee!!ee 12.0 eM!MeeM!Me 10 18 e!eMMeM!MeeM!MeMee!!eeM 12.0 PMMP\PMMP 12 19 PPMPMPMMP\PMMPPMPPPM 12.0 P!P\P!P 10 17 PP!PP!P\P!PPP!!PP 12.0 M!M\M!M 10 15 !MMM!M\M!MM!!M 12.0 X^kk^XX^kk^X 12 23 kX^kk^XX^kk^Xkk^kX^XXXXk 12.0 XW!WXXW!WX 10 23 XW!WXXW!WX!WXWW!XX!XWXW 12.0 WPrPWWPrPW 10 12 PWPPrWPWrPWrPrPWPrPWWPrPWrW 12.0 WPIPWWPIPW 10 13 PWPIPWIIPIWPWIIPIPWPIPWWPIPWWII 12.0 VPrPVVPrPV 10 11 PVPPrVPrPVrPVrPVVPrPVVPrPVr 12.0 VPIPVVPIPV 10 12 PVPIPVIIPIPVIIPVIPVVPIPVVPIPVII 12.0 UM8U8MUUM8U8MU 14 14 UMUUM888MU8MUM8U8MUUM8U8MU 12.0 UHtHUUHtHU 10 21 UHUtUHtHUUHtHUtHUtUUtHtHU 12.0 UHVHUUHVHU 10 23 UVHUUHVHUUHVHUVHUVVUVUVHVHU 12.0 UHOHUUHOHU 10 20 UOHUOUHOHUUHOHUHUOUOUHOHU 12.0 TcFcTTcFcT 10 16 FTFTcFcTTcFcTcTFFcT 12.0 PMKMPPMKMP 10 17 PPKMPMKPMKMPPMKMPPMPKPPM 12.0 PM!MPPM!MP 10 18 PP!MPMPM!MPPM!MPPMP!!PPM 12.0 P=EPE=PP=EPE=P 14 18 P==PPEEPEP=EPE=PP=EPE=PPEE= 12.0 OcFcOOcFcO 10 15 OFOFOcFcOOcFcOcFOFc 12.0 OTKTOOTKTO 10 11 OKTOKOTKOTKTOOTKTOT 12.0 OP!POOP!PO 10 22 POP!POOP!POP!POPPO!!POP 12.0 NUpUNNUpUN 10 13 UpUNUpNUpNUpUNNUpUNpUU 12.0 NU^UNNU^UN 10 13 U^UNU^NU^NU^UNNU^UNU^U 12.0 NUUNNUUN 10 13 UUNUNUNUUNNUUNUU 12.0 NUWUNNUWUN 10 16 UWUNUWNUWNUWUNNUWUNWUWWWU 12.0 NUTUNNUTUN 10 15 UUTNUNTUNUTUNNUTUNTUTTU 12.0 NUOUNNUOUN 10 14 UOUNOUNOUNUOUNNUOUNOUOU 12.0 NU+UNNU+UN 10 15 U+UNU+NU+NU+UNNU+UN+U++U 12.0 MPpPMMPpPM 10 15 PpPMPMpPMpMPpPMMPpPMPpPPM 12.0 MPWPMMPWPM 10 18 PWPMPMWPMWMPWPMMPWPMPWWPPWWM 12.0 MPTPMMPTPM 10 17 PPMTPMTPMMPTPMMPTPMPTTPTPM 12.0 MPOPMMPOPM 10 16 POPMPOMOPMMPOPMMPOPMPOPOPM 12.0 MHtHMMHtHM 10 20 HMtMHtHMMHtHMtHMtMtHtHM 12.0 MHlHMMHlHM 10 18 HMlMHlHMMHlHMHMllMHHM 12.0 MHVHMMHVHM 10 22 VHMMHVHMMHVHMVHMVVMVVHVHM 12.0 MHOHMMHOHM 10 19 OHMOMHOHMMHOHMHMOMOHOHM 12.0 M8K8MM8K8M 10 10 KMM8K88MK8MM8K8MM8K8M 12.0 KeFeKKeFeK 10 19 eFKeFeKKeFeKeeFeKFeeF 12.0 KDFDKKDFDK 10 16 FKDFDKKDFDKDFKFDF 12.0 K9F9KK9F9K 10 22 9F9K9F9KK9F9K999F99K9F9F9 12.0 G^kk^GG^kk^G 12 21 kG^kk^GG^kk^Gkk^Gk^GGk 12.0 G@kk@GG@kk@G 12 21 kG@kk@GG@kk@GkkGk@GG@k 12.0 G@ee@GG@ee@G 12 22 eG@ee@GG@ee@GeGe@eGeeG@ 12.0 G@^^@GG@^^@G 12 19 G@^^@GG@^^@G^G@^GG@ 12.0 G@!@GG@!@G 10 18 G@!@GG@!@G!G@G!!G@ 12.0 DM!MDDM!MD 10 15 !MDMDM!MDDM!MDM!D!M 12.0 @eVe@@eVe@ 10 23 Ve@eVe@@eVe@VVVeVe@Veee@V 12.0 @eFe@@eFe@ 10 20 eF@eFe@@eFe@eeF@eFeeF@ 12.0 @^kk^@@^kk^@ 12 20 k@^kk^@@^kk^@kk^k@^@k 12.0 =E@E==E@E= 10 14 ==@E@E@E=E@E==E@E=@EE= 12.0 =E/E==E/E= 10 13 //==/EE/E=E/E==E/E=EE= 12.0 8ece88ece8 10 17 eee888c8ece88ece8cceeec8 12.0 8M^M88M^M8 10 13 M^^M888M^8M^M88M^M8^8M 12.0 8MTM88MTM8 10 15 MTM888TM8MTM88MTM8TTT8M 12.0 8MOM88MOM8 10 14 OMOM88O8M8MOM88MOM8OO8M 12.0 8M(M88M(M8 10 12 M(M88(8M8M(M88M(M88M 12.0 6MKM66MKM6 10 16 6KMMK6MKM66MKM6MK666M 12.0 6M!M66M!M6 10 17 6!MM6M!M66M!M6M!!666M 12.0 +PMMP++PMMP+ 12 21 P+PMPM+PMMP++PMMP+PMP++P+PM 12.0 +P!P++P!P+ 10 19 P+P!P+P!P++P!P+PP++!!P+P 12.0 +M!M++M!M+ 10 17 +!MM+M!M++M!M+M++!!+M 11.294118 9P(9P9(P9P(9P9(P9 17 27 9P9P(9P9(P9P(9P9(P9P9P9999PP9 11.076923 kNUkUNkNUkUNk 13 16 UkUkNUkNUkNUkUNkNUkUNkUUk 11.076923 kMPkPMkMPkPMk 13 18 PkPMkPkMPMkMPkPMkMPkPMkPPPMk 11.076923 ^Ol^lO^Ol^lO^ 13 17 O^Ol^lO^Ol^lO^lO^O 11.076923 ZOTZTOZOTZTOZ 13 14 ZOTOZOTZZOTZTOZOTZTOZT 11.076923 ZKDZDKZKDZDKZ 13 19 ZKDZDKZKDZDKZDZZKDZ 11.076923 Ur9U9rUr9U9rU 13 23 9U9U9Ur9Ur9U9rUr9U9rU999U99rr9U 11.076923 P^kPk^P^kPk^P 13 24 PkP^kPk^P^kPk^PkPkP^kP^PPk 11.076923 P@^P^@P@^P^@P 13 22 PP@^P^@P@^P^@PPP^P@^P@P 11.076923 OX^O^XOX^O^XO 13 22 OX^O^XOX^O^XO^XO^XXOXX 11.076923 OXDODXOXDODXO 13 22 OXDODXOXDODXODXOXXDOXX 11.076923 OX6O6XOX6O6XO 13 24 OX6O6XOX6O6XO6XOXX6OX6X6 11.076923 OKDODKOKDODKO 13 18 OKDODKOKDODKODOKDO 11.076923 OG^O^GOG^O^GO 13 20 OG^O^GOG^O^GO^GO^GOG 11.076923 OG@O@GOG@O@GO 13 20 OG@O@GOG@O@GOG@OGOG@ 11.076923 O@^O^@O@^O^@O 13 19 O@^O^@O@^O^@O^@O^O@ 11.076923 Nr9N9rNr9N9rN 13 21 99N9r9Nr9N9rNr9N9rN99999rr9
And smokie, the algorithm finds much higher-scoring palindromic cycles in your test cipher:
L=4:
140.10811 #O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O%D%O# 37 39 #O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O% 100.0 1LTGTL11LTGTL11LTGTL11LTGTL11LTGTL1 35 37 1LTGTL11LTGTL11LTGTL11LTGTL11LTGTL11L 97.22222 |1LTTL1|1LTTL1|1LTTL1|1LTTL1|1LTTL1| 36 38 |1LTTL1|1LTTL1|1LTTL1|1LTTL1|1LTTL1|1L 96.77419 |LTGTL|LTGTL|LTGTL|LTGTL|LTGTL| 31 32 |LTGTL|LTGTL|LTGTL|LTGTL|LTGTL|L 96.77419 |1TGT1|1TGT1|1TGT1|1TGT1|1TGT1| 31 32 |1TGT1|1TGT1|1TGT1|1TGT1|1TGT1|1 96.77419 |1LGL1|1LGL1|1LGL1|1LGL1|1LGL1| 31 33 |1LGL1|1LGL1|1LGL1|1LGL1|1LGL1|1L 61.44 5F&4&F5F&4&F5F&4&F5F&4&F5 25 28 5F&4&F5F&4&F5F&4&F5F&4&F5F&4 61.44 .<*K*<.<*K*<.<*K*<.<*K*<. 25 28 .<*K*<.<*K*<.<*K*<.<*K*<.<*K 36.0 1LT5TL11LT5TL11LT5TL1 21 37 1LT5TL11LT5TL11LT5TL115LT5TL11LTTL11L 34.105263 |LT5TL|LT5TL|LT5TL| 19 32 |LT5TL|LT5TL|LT5TL|5LT5TL|LTTL|L 34.105263 |1T5T1|1T5T1|1T5T1| 19 32 |1T5T1|1T5T1|1T5T1|15T5T1|1TT1|1 34.105263 |1L_L1|1L_L1|1L_L1| 19 32 |1L_L1|1L_L1|1L_L1|1LL1|1LL1|1_L 34.105263 |1L5L1|1L5L1|1L5L1| 19 33 |1L5L1|1L5L1|1L5L1|15L5L1|1LL1|1L 34.105263 y:cMc:y:cMc:y:cMc:y 19 21 y:cMc:y:cMc:y:cMc:y:c 34.105263 cLTGTLcLTGTLcLTGTLc 19 20 LTGTccLLTGcTLcLTGTLcLTGTLcLTGTLcL 34.105263 _9tjt9_9tjt9_9tjt9_ 19 19 _9tjt9_9tjt9_9tjt9_ 34.105263 _9tMt9_9tMt9_9tMt9_ 19 19 _9tMt9_9tMt9_9tMt9_ 34.105263 UZzyzZUZzyzZUZzyzZU 19 19 yUZzyzZUZzyzZUZzyzZU 34.105263 UZzJzZUZzJzZUZzJzZU 19 19 UZzJzZUZzJzZUZzJzZU 34.105263 UZz>zZUZz>zZUZz>zZU 19 19 UZz>zZUZz>zZUZz>zZU 34.105263 HER>REHER>REHER>REH 19 21 HER>REHER>REHER>REHER 34.105263 5F&|&F5F&|&F5F&|&F5 19 28 |5F&|&F5F&|&F5F&|&F5F&&F5|F&| 34.105263 4&FcF&4&FcF&4&FcF&4 19 26 Fc&c4&FcF&4&FcF&4&FcF&4&FcF&c4 16.0 |zZdZz||zZdZz| 14 17 |Zzd|zZdZz||zZdZz|zZ| 16.0 |zZUZz||zZUZz| 14 18 |UZz|zZUZz||zZUZz|zZ|U 16.0 |z*K*z||z*K*z| 14 21 |*Kz*|z*K*z||z*K*z|*K*z|*K 16.0 |REHER||REHER| 14 20 |HER|REHER||REHER|REHE|R 16.0 fzZdZzffzZdZzf 14 17 ZfzdffzZdZzffzZdZzfzZf 16.0 fzZUZzffzZUZzf 14 18 UZfzffzZUZzffzZUZzfzZfU 16.0 Zz:y:zZZz:y:zZ 14 14 yZ:z:yz:ZZz:y:zZZz:y:zZ 16.0 Zz:q:zZZz:q:zZ 14 14 Z:z:z:ZZz:q:zZZz:q:zZ 16.0 Zz:V:zZZz:V:zZ 14 15 ZV:z:z:ZZz:V:zZZz:V:zZV 16.0 Zz:>:zZZz:>:zZ 14 14 Z:z:>z:ZZz:>:zZZz:>:zZ 16.0 Zz(y(zZZz(y(zZ 14 22 yZz(y(zZZz(y(zZ(Z(zy(zZ 16.0 Zz(_(zZZz(_(zZ 14 22 _Zz(_(zZZz(_(zZ(Z(z(zZ_ 16.0 Zz(J(zZZz(J(zZ 14 22 Zz(J(zZZz(J(zZ(Z(z(JzZ 16.0 Zz(.(zZZz(.(zZ 14 23 .Zz(.(zZZz(.(zZ(Z(z.(.zZ 16.0 TL|LTjTL|LTTL|LTjTL|LT 22 26 |LTjTL|LTjTL|LTTL|LTjTL|LTTL|L 16.0 TL|LTHTL|LTTL|LTHTL|LT 22 27 |LTHTL|LTHTL|LTTL|LTHTL|LTTHL|L 16.0 TL1J1LTTL1J1LT 14 32 1LTTL1J1LTTL1J1LTTL11LTTL11LTJTL11L 16.0 TL1>1LTTL1>1LT 14 19 1LTTL11>LTTL11LTTL1>1LTTL1>1LTTL11L 16.0 TL181LTTL181LT 14 36 1LT8TL181LTTL181LTTL1818LT8TL181LTTL11L8 16.0 TL141LTTL141LT 14 27 1LTTL411LTTL141LTTL141LT4TL11LTTL11L4 16.0 T1|1TjT1|1TT1|1TjT1|1T 22 26 |1TjT1|1TjT1|1TT1|1TjT1|1TT1|1 16.0 T1|1THT1|1TT1|1THT1|1T 22 27 |1THT1|1THT1|1TT1|1THT1|1TTH1|1 16.0 RLTGTLRRLTGTLR 14 15 LTGTRLLRTGRTLLTGTLRLTGTLRRLTGTLRL 16.0 RLT;TLRRLT;TLR 14 16 LTT;RLLRTRTLLTTLRLT;TLRRLT;TLRL; 16.0 OF&|&FOOF&|&FO 14 27 O|OFO&O|&FOF&|&FOOF&|&FOF&&OFOO|FO&O| 16.0 OF&4&FOOF&4&FO 14 27 OOFO&O4&FOF&4&FOOF&4&FOF&4&OFOOFO&O4 16.0 OF&(&FOOF&(&FO 14 28 OOFO&(O&F(OF&(&FOOF&(&FOF(&&OF(OOF(O&O 16.0 O%D%OlO%D%OO%D%OlO%D%O 22 31 O%D%OO%D%OlO%D%OO%D%OlO%D%OlO%D%OOl% 16.0 O%D%OVO%D%OO%D%OVO%D%O 22 36 O%D%OVO%D%OO%D%OVO%D%OO%D%OOV%D%OOV% 16.0 O%D%OSO%D%OO%D%OSO%D%O 22 24 O%DS%OO%D%OO%D%OSO%D%OO%D%OSO%D%OO% 16.0 LTGTLSLTGTLLTGTLSLTGTL 22 23 SLTGTLLTGTLSLTGTLLTGTLSLTGTLL 16.0 LTGTL>LTGTLLTGTL>LTGTL 22 29 LTGTL>LTGTLLTGTL>LTGTL>LTGTLL 16.0 LTGTL.LTGTLLTGTL.LTGTL 22 24 .LTGT.LLTGTL.LTGTLLTGTL.LTGTL.L 16.0 L1|1LqL1|1LL1|1LqL1|1L 22 22 |1LL1|1LL1|1LqL1|1LL1|1LqL1|1L 16.0 L1|1LjL1|1LL1|1LjL1|1L 22 27 |1LjL1|1LjL1|1LL1|1LjL1|1LL1|1L 16.0 L1|1LML1|1LL1|1LML1|1L 22 27 |1LML1|1LML1|1LL1|1LML1|1LL1|1L 16.0 L1|1LKL1|1LL1|1LKL1|1L 22 29 |1KLL1|1LKL1|1LL1|1LKL1|1LKL1|1LK 16.0 L1|1LHL1|1LL1|1LHL1|1L 22 28 |1LHL1|1LHL1|1LL1|1LHL1|1LHL1|1L 16.0 F&4&FUF&4&FF&4&FUF&4&F 22 26 UF&4&FUF&4&FF&4&FUF&4&FF&U4 16.0 :c*K*c::c*K*c: 14 21 *K:c*c::c*K*c::c*K*c:*K*:c*K 16.0 :O%D%O::O%D%O: 14 34 O%D%O:O%D%O::O%D%O:O%:D%OO%D%O:O%D%O:O% 16.0 9t%D%t99t%D%t9 14 28 %D%9t%D%t99t%D%t9%D9%t%D%%D%t9% 16.0 3F&4&F33F&4&F3 14 18 F&43&F3F&4&F3F&4&F33F&4&F33F&4 16.0 1|1ZdZ1|11|1ZdZ1|1 18 22 |1Zd1|1ZdZ1|11|1ZdZ1|11Z|1 16.0 1|1ZUZ1|11|1ZUZ1|1 18 23 |1UZ1|1ZUZ1|11|1ZUZ1|11Z|1U 16.0 1|1*K*1|11|1*K*1|1 18 26 |*1K*1|1*K*1|11|1*K*1|1*K*1|1*K 16.0 1LfjfL11LfjfL1 14 32 1LfjfL11LfjfL1f1LL11LjL11LfL1f1L 16.0 1LfdfL11LfdfL1 14 32 1LfdfL11LfdfL1f1LL11dLL11LfL1f1L 16.0 1LTjTL11LTjTL1 14 35 1LTjTL11LTjTL11LTTL11LTjTL11LTTL11L 16.0 1LTHTL11LTHTL1 14 36 1LTHTL11LTHTL11LTTL11LTHTL11LTTHL11L 16.0 1LT;TL11LT;TL1 14 17 1LTT;L11LTTL11LTTL11LT;TL11LT;TL11L; 16.0 1LT:TL11LT:TL1 14 31 1LT:TL:11LT:TL11LT:TL1:1LTTL1:1LTTL:11L 16.0 *c:y:c**c:y:c* 14 23 *y:c*c:y:c**c:y:c**c:y**:c* 16.0 *c:_:c**c:_:c* 14 23 *_:c*c:_:c**c:_:c**c:**:c_* 16.0 *c:>:c**c:>:c* 14 23 *:c*c:>:c**c:>:c**c:>**:c* 16.0 *L1|1L**L1|1L* 14 14 |*1L*L1|1L**L1|1LL1|1*L*L1|1L**L1|1L* 16.0 *L1l1L**L1l1L* 14 14 *1L*L1l1L**L11LL11*Ll*L1l1L**L1l1L* 16.0 *L1c1L**L1c1L* 14 14 *1Lc*cL11Lc**L1c1LL11c*L*L1c1L**L1c1L* 16.0 %L1|1L%%L1|1L% 14 35 |%1L%%%L1|1L%%L1|1L%L1|1%L%%L1|1%L%L1|1L% 16.0 %L1J1L%%L1J1L% 14 33 %1L%%%L1J1L%%L1J1L%L11%L%%L11%L%JL11L% 16.0 %L181L%%L181L% 14 37 %1L%8%%L181L%%L181L%L1818%L8%%L181%L%L11L%8 15.304348 pF&4&FF&4&FpF&4&FF&4&Fp 23 27 pF&4&FF&4&FpF&4&FF&4&FpFp&4 15.304348 VF&4&FF&4&FVF&4&FF&4&FV 23 27 VF&4&FF&4&FVF&4&FF&4&FVF&V4 15.304348 SF&4&FF&4&FSF&4&FF&4&FS 23 26 SF&4&FF&4&FSF&4&FF&4&FSF&4 15.304348 /LTGTLLTGTL/LTGTLLTGTL/ 23 24 LT/G/TL/LTGTLLTGTL/LTGTLLTGTL/L 15.238095 pF&&FUF&&FpF&&FUF&&Fp 21 25 UpF&&FUF&&FpF&&FUF&&FpFp&U 15.238095 VF&&FUF&&FVF&&FUF&&FV 21 25 UVF&&FUF&&FVF&&FUF&&FVF&VU 15.238095 SLTTL>LTTLSLTTL>LTTLS 21 27 SLTTL>LTTLSLTTL>LTTLS>LTTLL 15.238095 KV<.<K<.<VKV<.<K<.<VK 21 21 .<KV<.<K<.<VKV<.<K<.<VK 15.238095 /LTTLSLTTL/LTTLSLTTL/ 21 22 SLT//TL/LTTLSLTTL/LTTLSLTTL/L 15.058824 tfzZtZzftfzZtZzft 17 20 tZfzftfzZtZzftfzZtZzftzZf 15.058824 pF4FUF4FpF4FUF4Fp 17 21 UpF4FUF4FpF4FUF4FpFpU4 15.058824 p&4&l&4&p&4&l&4&p 17 22 p&4&l&4&p&4&l&4&plp&l4 15.058824 p&4&U&4&p&4&U&4&p 17 21 Up&4&U&4&p&4&U&4&pp&U4 15.058824 Y*G2*2G*Y*G2*2G*Y 17 21 Y*G2*2G*Y*G2*2G*Y**G* 15.058824 VF4FUF4FVF4FUF4FV 17 21 UVF4FUF4FVF4FUF4FVFVU4 15.058824 V&4&^&4&V&4&^&4&V 17 21 ^V&4&^&4&V&4&^&4&V^&V4
L=3:
108.0 O%D%OO%D%OO%D%OO%D%OO%D%OO%D%O 30 32 O%D%OO%D%OO%D%OO%D%OO%D%OO%D%OO% 108.0 %O#O%%O#O%%O#O%%O#O%%O#O%%O#O% 30 30 #O%%O#O%%O#O%%O#O%%O#O%%O#O%%O#O% 103.68 #ODO#ODO#ODO#ODO#ODO#ODO# 25 26 #ODO#ODO#ODO#ODO#ODO#ODO#O 103.68 #%D%#%D%#%D%#%D%#%D%#%D%# 25 26 #%D%#%D%#%D%#%D%#%D%#%D%#% 75.0 LTGTLLTGTLLTGTLLTGTLLTGTL 25 26 LTGTLLTGTLLTGTLLTGTLLTGTLL 75.0 L1|1LL1|1LL1|1LL1|1LL1|1L 25 25 |1LL1|1LL1|1LL1|1LL1|1LL1|1L 75.0 1TGT11TGT11TGT11TGT11TGT1 25 26 1TGT11TGT11TGT11TGT11TGT11 75.0 1LTTL11LTTL11LTTL11LTTL11LTTL1 30 32 1LTTL11LTTL11LTTL11LTTL11LTTL11L 75.0 1LGL11LGL11LGL11LGL11LGL1 25 27 1LGL11LGL11LGL11LGL11LGL11L 72.11538 |LTTL|LTTL|LTTL|LTTL|LTTL| 26 27 |LTTL|LTTL|LTTL|LTTL|LTTL|L 72.11538 |1TT1|1TT1|1TT1|1TT1|1TT1| 26 27 |1TT1|1TT1|1TT1|1TT1|1TT1|1 71.42857 |TGT|TGT|TGT|TGT|TGT| 21 21 |TGT|TGT|TGT|TGT|TGT| 71.42857 |LGL|LGL|LGL|LGL|LGL| 21 22 |LGL|LGL|LGL|LGL|LGL|L 71.42857 |1G1|1G1|1G1|1G1|1G1| 21 22 |1G1|1G1|1G1|1G1|1G1|1 48.0 F&4&FF&4&FF&4&FF&4&F 20 23 F&4&FF&4&FF&4&FF&4&FF&4 48.0 <*K*<<*K*<<*K*<<*K*< 20 23 <*K*<<*K*<<*K*<<*K*<<*K 48.0 *<.<**<.<**<.<**<.<* 20 20 .<**<.<**<.<**<.<**<.<* 48.0 &FcF&&FcF&&FcF&&FcF& 20 21 Fc&c&FcF&&FcF&&FcF&&FcF&c 48.0 &F5F&&F5F&&F5F&&F5F& 20 20 5F&&F5F&&F5F&&F5F&&F5F& 45.17647 5F4F5F4F5F4F5F4F5 17 19 5F4F5F4F5F4F5F4F5F4 45.17647 5&4&5&4&5&4&5&4&5 17 19 5&4&5&4&5&4&5&4&5&4 45.17647 .<K<.<K<.<K<.<K<. 17 19 .<K<.<K<.<K<.<K<.<K 45.17647 .*K*.*K*.*K*.*K*. 17 19 .*K*.*K*.*K*.*K*.*K 27.0 c:y:cc:y:cc:y:c 15 15 y:cc:y:cc:y:cc:y:c 27.0 c:>:cc:>:cc:>:c 15 15 :cc:>:cc:>:cc:>:c 27.0 ZzyzZZzyzZZzyzZ 15 15 yZzyzZZzyzZZzyzZ 27.0 ZzJzZZzJzZZzJzZ 15 15 ZzJzZZzJzZZzJzZ 27.0 Zz>zZZz>zZZz>zZ 15 15 Zz>zZZz>zZZz>zZ 27.0 TLcLTTLcLTTLcLT 15 19 LTTccLLTcTLcLTTLcLTTLcLTTLcL 27.0 TL4LTTL4LTTL4LT 15 24 LTTL4LTTL4LTTL4LT4TLLTTLL4 27.0 T&|&TT&|&TT&|&T 15 23 |TT&|&TT&|&TT&|&T&&T|TT&| 27.0 T&4&TT&4&TT&4&T 15 23 TT&4&TT&4&TT&4&T&4&TTT&4 27.0 REHERREHERREHER 15 15 HERREHERREHERREHER 27.0 LT5TLLT5TLLT5TL 15 26 LT5TLLT5TLLT5TL5LT5TLLTTLL 27.0 F&|&FF&|&FF&|&F 15 23 |F&|&FF&|&FF&|&FF&&F|F&| 27.0 ER>REER>REER>RE 15 17 ER>REER>REER>REER 27.0 :cMc::cMc::cMc: 15 17 :cMc::cMc::cMc::c 27.0 9tjt99tjt99tjt9 15 15 9tjt99tjt99tjt9 27.0 9tMt99tMt99tMt9 15 15 9tMt99tMt99tMt9 27.0 1T5T11T5T11T5T1 15 26 1T5T11T5T11T5T115T5T11TT11 27.0 1L_L11L_L11L_L1 15 26 1L_L11L_L11L_L11LL11LL11_L 27.0 1L5L11L5L11L5L1 15 27 1L5L11L5L11L5L115L5L11LL11L 27.0 %D%V%D%%D%V%D%%D%V%D% 21 23 %D%V%D%%D%V%D%%D%V%D%V% 25.578949 OTLOLTOTLOLTOTLOLTO 19 30 OLTOOTLOLTOTLOLTOTLOLTOTOLOLTTLOOL 25.3125 _9tt9_9tt9_9tt9_ 16 16 _9tt9_9tt9_9tt9_ 25.3125 UZzzZUZzzZUZzzZU 16 16 UZzzZUZzzZUZzzZU 24.923077 |T5T|T5T|T5T| 13 21 |T5T|T5T|T5T|5T5T|TT| 24.923077 |L_L|L_L|L_L| 13 21 |L_L|L_L|L_L|LL|LL|_L 24.923077 |L5L|L5L|L5L| 13 22 |L5L|L5L|L5L|5L5L|LL|L 24.923077 |1p1|1p1|1p1| 13 14 |1p1|11|1p1|1p1|1p1|1 24.923077 |1_1|1_1|1_1| 13 21 |1_1|1_1|1_1|11|11|1_ 24.923077 |151|151|151| 13 22 |151|151|151|1551|11|1 24.923077 ycMcycMcycMcy 13 14 ycMcycMcycMcyc 24.923077 y:j:y:j:y:j:y 13 14 y:j:y:j:y:j:y: 24.923077 y:d:y:d:y:d:y 13 14 y:d:y:d:y:d:y: 24.923077 y:M:y:M:y:M:y 13 14 y:M:y:M:y:M:y: 24.923077 cTGTcTGTcTGTc 13 13 TGTccTGcTcTGTcTGTcTGTc 24.923077 cLGLcLGLcLGLc 13 14 LGccLLGcLcLGLcLGLcLGLcL 24.923077 _tjt_tjt_tjt_ 13 13 _tjt_tjt_tjt_ 24.923077 _tMt_tMt_tMt_ 13 13 _tMt_tMt_tMt_ 24.923077 _9j9_9j9_9j9_ 13 13 _9j9_9j9_9j9_ 24.923077 _9d9_9d9_9d9_ 13 13 _9d9_9d9_9d9_ 24.923077 _9M9_9M9_9M9_ 13 13 _9M9_9M9_9M9_ 24.923077 _9J9_9J9_9J9_ 13 13 _9J9_9J9_9J9_ 24.923077 UzyzUzyzUzyzU 13 13 yUzyzUzyzUzyzU 24.923077 UzJzUzJzUzJzU 13 13 UzJzUzJzUzJzU 24.923077 Uz>zUz>zUz>zU 13 13 Uz>zUz>zUz>zU 24.923077 UZyZUZyZUZyZU 13 13 yUZyZUZyZUZyZU 24.923077 UZjZUZjZUZjZU 13 13 UZjZUZjZUZjZU 24.923077 UZMZUZMZUZMZU 13 13 UZMZUZMZUZMZU 24.923077 UZJZUZJZUZJZU 13 13 UZJZUZJZUZJZU 24.923077 UZ>ZUZ>ZUZ>ZU 13 13 UZ>ZUZ>ZUZ>ZU 24.923077 K*y*K*y*K*y*K 13 16 *yK*y*K*y*K*y*K**K 24.923077 K*p*K*p*K*p*K 13 13 *Kp**K*p*K*p*K*p*K 24.923077 K*V*K*V*K*V*K 13 13 *KV**K*V*K*V*K*V*K 24.923077 K*C*K*C*K*C*K 13 13 *K**K*C*K*C*K*C*K 24.923077 K*>*K*>*K*>*K 13 16 *K*>*K*>*K*>*K**K 24.923077 HR>RHR>RHR>RH 13 14 HR>RHR>RHR>RHR 24.923077 HEyEHEyEHEyEH 13 14 yHEyEHEyEHEyEHE 24.923077 HE>EHE>EHE>EH 13 14 HE>EHE>EHE>EHE 24.923077 HE.EHE.EHE.EH 13 15 .HE.EHE.EHE.EH.E 24.923077 DTGTDTGTDTGTD 13 21 DTGTDTGTDTGTDTGDTDTGT 24.923077 DT5TDT5TDT5TD 13 21 DT5TDT5TDT5TD5T5DTDTT 24.923077 D%G%D%G%D%G%D 13 19 %DG%%D%G%D%G%D%G%D%%D%G% 24.923077 D%5%D%5%D%5%D 13 23 %D%5%D%5%D%5%D%55%D%%D%% 24.923077 BO#OBO#OBO#OB 13 16 #OOB#OOB#OBBO#OBO#OBO#OBO#O 24.923077 5F|F5F|F5F|F5 13 19 |5F|F5F|F5F|F5FF5|F| 24.923077 5F(F5F(F5F(F5 13 16 5F(F(5F(F5F(F5F(F5(F( 24.923077 5&|&5&|&5&|&5 13 19 |5&|&5&|&5&|&5&&5|&| 24.923077 4FcF4FcF4FcF4 13 18 Fcc4FcF4FcF4FcF4FcFc4 24.923077 4&c&4&c&4&c&4 13 18 c&c4&c&4&c&4&c&4&c&c4 24.923077 .<d<.<d<.<d<. 13 17 .<d<.<d<.<d<.<<.< 24.923077 .<U<.<U<.<U<. 13 18 .<U<.<U<.<U<.<<.<U 24.923077 #OdO#OdO#OdO# 13 20 #OO#OdO#OdO#OdO#OO#OO#O 24.923077 #ONO#ONO#ONO# 13 26 #ONO#ONO#ONO#NONO#OO#OO#NO 12.0 |zjz||zjz| 10 12 |jz|zjz||zjz|z| 12.0 |zdz||zdz| 10 12 |zd|zdz||zdz|z| 12.0 |zZZz||zZZz| 12 15 |Zz|zZZz||zZZz|zZ| 12.0 |zUz||zUz| 10 13 |Uz|zUz||zUz|z|U 12.0 |zKz||zKz| 10 14 |Kz|zKz||zKz|Kz|K
So I think I can conclude from this that Z340 and Z408 do not show strong palindromic cycles in their encoding.
I am still mystified by "+F+FF+++++F++F+".
Sorry I did not have a chance to convert symbols to numbers. Here is the symbolic version of your cipher that I’m using:
#.OW|Y%<*DyNS1U7K LpT^H/_G%5O9tZf-V B2/:#FOj)z8Td-c&( EMW%*<Dc+;%.PNRfL O:4B12J38|t&l1^>/ 9L)Ry#_F(Tfz95kE: +G3Z-tHcO)E<UdR*K FZY%*<jzfT&BDMN+% CLt)14(|fJ9&FB8O. <#cN1@SL3T:VGO5%_ TqLyp1F&|84(>:+1& FDcNbz/38Z^W9U2dX %5BR+O3*F(LlTt&7E 84Z2#&OjFBH5;(GM% PDT%XOK*pL31lz8c# :SE3RkOV|>yPR<.FB 1%(ECLYD<*Tk;%K*p G^J)TfAt<HqL9OX#. <:z&NOC1bZ-)AcEf| l1VR/_LbU-;%*K48A
HAPPY NEW YEAR, EVERYBODY!
Doranchak, I see that you posted above as I was drafting this and will drop back to read more thoroughly.
++++
+F+FF+++++F++F+
+F+FF+++++F++F+
I think that this is very interesting because the + and F, if I add up all of the cycle scores for every symbol, rank among the lowest. And it takes about 1000 shuffles to get something like this.
A message that is shuffled is going to be as regular cyclic as a message with 100% random symbol selection. But we know he did not do that. A message with all perfect regular cycles will also have a lot of false cycles created by the perfect cycles running concurrently with each other. But we know he did not do that either. And we have evidence that whatever he did, it created more, longer, unique symbol strings.
A look at the regular cyclic nature of the + symbol. The + regular cycles with the B here, but this can also be replicated very easily with a few random shuffles, and is the highest scoring + cycle.
+ B B + + + + + + + + + + B + + B + B + B + B + + B + B + + B + + B B +
Here is an interesting longer symmetry, however, with the B symbol.
+ B B + + + + + + + + + + B + + B + B + B + B + + B + B + + B + + B B +
If I add up all of the cycle scores for each symbol, the B also ranks among the lowest.
Here is the most cyclic with B, but still not necessarily a true cycle:
B B 5 5 B B 5 B 5 B 5 B 5 B 5 B B B B
But, here are a couple of symmetries that are very interesting:
B B B 6 B B B 6 B B B 6 B B B
and
H B B H B B B B B B B B H B B H
Which could be true and partly responsible for what Jarlve is seeing here:
Back to the F. The highest scoring and uninteresting two symbol cycle is this one:
O O F F O F O F O F O F F F O F O F O O
But then check out this one:
F / F F F F / F F F F / F
And this one, when read right left just like the interesting and longest repeating sequence with the + and F, has a repeating sequence and the leftover symbol is at left:
M M F F F M F F M M F F F M F F M
So I wonder what created this:
++++
+F+FF+++++F++F+
+F+FF+++++F++F+
Maybe he was feeling creative and instead of using regular cycles, encoded different plaintext with different patterns. Maybe some or all above are true or false. But the mechanism created more, longer unique sequence strings.
Here is a very rough idea. Use the locations of unique strings or repeating multiple symbol patterns or symmetries to narrow down the areas of the message that are and are not part of a transposition.
See this:
Let’s for the sake of argument, although he could have done many things, he used a complete inscription rectangle with 15 rows but we don’t know how many columns. And he transposed the plaintext before adding nulls instead of after adding nulls. 340 is not a multiplier of 15, so there are nulls in there. And we know that only three nulls can make an untransposed plaintext unreadable, not even taking into consideration homophonic encoding. And he encoded the transposed plaintext before adding the nulls, which are just gibberish homophonic symbols instead of adding null plaintext and then encoding.
Could the study of patterns in a message help us identify the areas of a message that are or are not part of a transposition scheme? Because we have this:
++++
+F+FF+++++F++F+
+F+FF+++++F++F+
And this:
M
M F F F M F F M
M F F F M F F M
Could he have encoded right left bottom top, then filled in gibberish symbols? Or could the part of the message with the ++++ be part of a different scheme? Just a very rough idea.
It is difficult for me to accept that this is just a random occurrence. Maybe it is intentional, or maybe it is the product of other concurrent symmetrical cycles. I drafted the message into a bunch of different column widths last night, wondering if you found parts of repeated transposed words. But I didn’t see any patterns. You may want to check that though.
I have to remake my encoder spreadsheet pretty much from scratch because as I added to it over time, without anticipating the changes, it just became more and more messy. My next one is going to allow for different encoding patterns.
I made some changes to my palindrome finding algorithm and it found some palindromic cycles in Z340 for L=4. Columns are: score, palindromic sequence, sequence length, full string length, full string:
14.769231 /p(;(p/p(;(p/ 13 17 pp((ppp/p(;(p/p(;(p/(pp; 14.769231 /p(X(p/p(X(p/ 13 16 pp((ppp/p(X(p/p(X(p/(pp 14.769231 ;N-7-N;N-7-N; 13 13 N7-;N-7-N;N-7-N; 14.769231 .cU7Uc.cU7Uc. 13 24 .cU7Uc.cU7Uc.c.cUc..cc7c 14.769231 /pK;Kp/pK;Kp/ 13 17 ppKpppK/pK;Kp/pK;Kp/ppK; 14.769231 /pKXKp/pKXKp/ 13 16 ppKpppK/pKXKp/pKXKp/ppK 14.769231 /pKZKp/pKZKp/ 13 17 ppKZpppK/pKZKp/pKZKp/ppZK 14.769231 NcU7UcNcU7UcN 13 23 NcU7UcNcU7UcNcNcUccc7cNAnd for L=3:
24.923077 ^c9c^c9c^c9c^ 13 16 ^c^9^c9c^c9c^c9c^ccc 24.923077 DKZKDKZKDKZKD 13 15 DKZKDKZKDKZKDZK 12.0 y|D|yy|D|y 10 17 |Dy|D|yy|D|y|y|||D| 12.0 y5D5yy5D5y 10 15 Dy5D5yy5D5y55y5D 12.0 pp(.(pppp(.(pp 14 24 pp(.(pppp(.(pp.(..(p.(pp 12.0 pp(%(pppp(%(pp 14 20 pp(%(pppp(%(pp((p(pp 12.0 pp#f#pppp#f#pp 14 20 pp#f#pppp#f#pp#fpfpp 12.0 pp#.#pppp#.#pp 14 22 pp#.#pppp#.#pp.#..p.pp 12.0 pp#%#pppp#%#pp 14 18 pp#%#pppp#%#pp#ppp 12.0 pl;lppl;lp 10 14 plppplppl;lppl;lplpp; 12.0 pl6lppl6lp 10 14 plppplppl6lppl6lp6lpp 12.0 pKfKppKfKp 10 14 ppKfpppKpKfKppKfKpfppK 12.0 pKZKppKZKp 10 14 ppKZpppKpKZKppKZKpppZK 12.0 pKXKppKXKp 10 13 ppKpppKpKXKppKXKpppK 12.0 pK;KppK;Kp 10 14 ppKpppKpK;KppK;KpppK; 12.0 pK6KppK6Kp 10 14 ppKpppKpK6KppK6Kp6ppK 12.0 p(X(pp(X(p 10 13 pp((pppp(X(pp(X(p(pp 12.0 p(;(pp(;(p 10 14 pp((pppp(;(pp(;(p(pp; 12.0 lptpllptpl 10 17 plppplptpllptplltplptp 12.0 lp/pllp/pl 10 16 plppplp/pllp/pllpl/pp 12.0 lLfLllLfLl 10 17 lLfLllLfLlllffLlL 12.0 lLYLllLYLl 10 17 lLYLllLYLlYllLlLY 12.0 lLNLllLNLl 10 18 lLNLllLNLllNlNLlLN 12.0 lG.GllG.Gl 10 19 lG.GllG.Gll.lG...Gl 12.0 l(U(ll(U(l 10 19 l(U(ll(U(lUUl(lU(l( 12.0 l(.(ll(.(l 10 20 l(.(ll(.(ll.(l..(.l( 12.0 l(%(ll(%(l 10 16 l(%(ll(%(ll(l(l( 12.0 l#f#ll#f#l 10 16 l#f#ll#f#ll#lffl 12.0 l#U#ll#U#l 10 17 l#U#ll#U#lUUl#lUl 12.0 l#.#ll#.#l 10 18 l#.#ll#.#ll.#l...l 12.0 l#%#ll#%#l 10 14 l#%#ll#%#ll#ll 12.0 dz_zddz_zd 10 17 dz_zddz_zdzzzzd_z 12.0 dzJzddzJzd 10 18 dzJzddzJzdzJJzzzdz 12.0 d(c(dd(c(d 10 22 d(c(dd(c(dccc(cc(cc(dc 12.0 d(U(dd(U(d 10 17 d(U(dd(U(dUU(U((d 12.0 d(.(dd(.(d 10 18 d(.(dd(.(d.(..(.(d 12.0 d(%(dd(%(d 10 14 d(%(dd(%(d(((d 12.0 d#f#dd#f#d 10 14 d#f#dd#f#d#ffd 12.0 d#c#dd#c#d 10 20 d#c#dd#c#dcc#cccccdc 12.0 d#U#dd#U#d 10 15 d#U#dd#U#dUU#Ud 12.0 d#.#dd#.#d 10 16 d#.#dd#.#d.#...d 12.0 d#%#dd#%#d 10 12 d#%#dd#%#d#d 12.0 cU7UccU7Uc 10 18 cU7UccU7UcccUccc7c 12.0 cKtKccKtKc 10 20 KcKtKccKtKccctcKcctcK 12.0 cKDKccKDKc 10 19 DKcKDKccKDKccccKcccDK 12.0 cK/KccK/Kc 10 19 KcK/KccK/KccccKcc/cK 12.0 ^ptp^^ptp^ 10 16 p^ppp^ptp^^ptp^tp^ptp 12.0 ^p/p^^p/p^ 10 15 p^ppp^p/p^^p/p^p^/pp 12.0 ^LfL^^LfL^ 10 16 ^LfL^^LfL^^f^fLL 12.0 ^LYL^^LYL^ 10 16 ^LYL^^LYL^Y^^LLY 12.0 ^LNL^^LNL^ 10 17 ^LNL^^LNL^NN^^LLN 12.0 ^G.G^^G.G^ 10 18 ^G.G^^G.G^.G^..^.G 12.0 ^(.(^^(.(^ 10 19 ^(.(^^(.(^.(^..(^.( 12.0 ^#f#^^#f#^ 10 15 ^#f#^^#f#^#^f^f 12.0 ^#.#^^#.#^ 10 17 ^#.#^^#.#^.#^..^. 12.0 ^#%#^^#%#^ 10 13 ^#%#^^#%#^#^^ 12.0 YfXfYYfXfY 10 10 YfXfYYfXfY 12.0 Yf>fYYf>fY 10 11 >Yf>fYYf>fY> 12.0 Yf:fYYf:fY 10 10 Yf:fYYf:fY 12.0 Yf3fYYf3fY 10 10 Yf3fYYf3fY 12.0 VptpVVptpV 10 16 pVpppVptpVVptpVtVpptp 12.0 Vp/pVVp/pV 10 15 pVpppVp/pVVp/pVVp/pp 12.0 VLfLVVLfLV 10 16 VLfLVVLfLVfVVfLL 12.0 VLYLVVLYLV 10 16 VLYLVVLYLVYVVLLY 12.0 VLNLVVLNLV 10 17 VLNLVVLNLVNNVVLLN 12.0 U2f2UU2f2U 10 12 2fU222U2f2UU2f2Uf2 12.0 U2#2UU2#2U 10 11 2#U#22#2U2#2UU2#2U2 12.0 TfXfTTfXfT 10 11 TfXfTTfXfTT 12.0 TfCfTTfCfT 10 14 TfCfTTfCfTCCTC 12.0 Tf>fTTf>fT 10 12 >Tf>fTTf>fTT> 12.0 Tf:fTTf:fT 10 11 Tf:fTTf:fTT 12.0 Tf3fTTf3fT 10 11 Tf3fTTf3fTT 12.0 TN;NTTN;NT 10 13 TN;NTTN;NTTN; 12.0 T9X9TT9X9T 10 11 T9X9TT9X9TT 12.0 T9;9TT9;9T 10 12 T9;9TT9;9TT; 12.0 ROfORROfOR 10 22 ROfORROfORORORRfOfROOO 12.0 ROcORROcOR 10 28 ROcORROcORcOROcRcRccORccOOcO 12.0 ROUORROUOR 10 23 ROUORROUORUOURORRUOROOO 12.0 ROJORROJOR 10 22 ROJORROJORJORORJROROOO 12.0 RODORRODOR 10 22 RODORRODORORDORROROODO 12.0 RO.ORRO.OR 10 24 RO.ORRO.OROROR.R..O.ROOO 12.0 RO%ORRO%OR 10 20 RO%ORRO%ORORORROROOO 12.0 RLfLRRLfLR 10 18 RLfLRRLfLRRRRffRLL 12.0 RLYLRRLYLR 10 18 RLYLRRLYLRRYRRRLLY 12.0 RLNLRRLNLR 10 19 RLNLRRLNLRRRNRNRLLN 12.0 RG.GRRG.GR 10 20 RG.GRRG.GRRR.RG...GR 12.0 RFzFRRFzFR 10 17 RzRzFRFFzzRFzFRRFzFRFzRFzFz 12.0 RF6FRRF6FR 10 15 RRFRFFRF6FRRF6FRFR6FF 12.0 R(c(RR(c(R 10 25 R(c(RR(c(RcRcRc(Rcc(Rcc(c 12.0 R(U(RR(U(R 10 20 R(U(RR(U(RUURR(RU(R( 12.0 R(.(RR(.(R 10 21 R(.(RR(.(RRR.(R..(.R( 12.0 R(%(RR(%(R 10 17 R(%(RR(%(RRR(R(R( 12.0 R#f#RR#f#R 10 17 R#f#RR#f#RRR#RffR 12.0 R#c#RR#c#R 10 23 R#c#RR#c#RcRcR#cRccRccc 12.0 R#U#RR#U#R 10 18 R#U#RR#U#RUURR#RUR 12.0 R#.#RR#.#R 10 19 R#.#RR#.#RRR.#R...R 12.0 R#%#RR#%#R 10 15 R#%#RR#%#RRR#RR 12.0 Np/pNNp/pN 10 11 pNpppp/pNp/pNNp/pNp 12.0 N2E2NN2E2N 10 10 E2N2222N2E2NN2E2N 12.0 N-7-NN-7-N 10 10 N7-N-7-NN-7-NBut many similar sequences are found for Z408 L=4:
16.0 PM!MP\PM!MP 14 23 PP!MPMPM!MP\PM!MPPMP!!PPM 16.0 G@^kk^@GG@^kk^@G 16 27 kG@^kk^@GG@^kk^@Gkk^Gk@^GG@k 16.0 +PM!MP++PM!MP+ 14 25 P+P!MPM+PM!MP++PM!MP+PMP++!!P+PM 15.058824 P@^kPk^@P@^kPk^@P 17 30 PkP@^kPk^@P@^kPk^@PkPkP^kP@^P@Pk 15.058824 OG@^O^@GOG@^O^@GO 17 26 OG@^O^@GOG@^O^@GO^G@O^GOG@ 14.769231 TPMKMPTPMKMPT 13 23 PPKMTPMKTPMKMPTPMKMPTPMPTKTPTPM 14.769231 TPM!MPTPM!MPT 13 24 PP!MTPMTPM!MPTPM!MPTPMPTT!!PTPM 14.769231 OPMKMPOPMKMPO 13 22 POPKMPOMKOPMKMPOPMKMPOPMPOKPOPM 14.769231 OPM!MPOPM!MPO 13 23 POP!MPOMOPM!MPOPM!MPOPMPO!!POPM 14.769231 K8M(M8K8M(M8K 13 15 KM(M8K8(8MK8M(M8K8M(M8K8M 14.769231 Gr9(9rGr9(9rG 13 23 9G9(9rG9(Gr9(9rGr9(9rG999G99Grr9 14.769231 /r9(9r/r9(9r/ 13 21 9//9(/9r9(/r9(9r/r9(9r/99999rr9 14.769231 !8M(M8!8M(M8! 13 16 !M(M88(8M!8M(M8!8M(M8!!8M 8.533334 pHELpHELEHpLEHp 15 31 pHELpHELEHpLEHpLHLEHLpEpELHLEEH 8.533334 pH#LpH#L#HpL#Hp 15 32 pH#LpH#L#HpL#HpLHLHLp##p##LHL##H 8.533334 eDLpeDLpLDepLDe 15 28 peeDLpeDLpLDepLDeLLpeDpeeLDLee 8.533334 eDLZeDLZLDeZLDe 15 30 ZeeDLZeDLZLDeZLDeLLZeDZeZeLDLeeZ 8.533334 eDLWeDLWLDeWLDe 15 31 WeeDLWeDLWLDeWLDeLLWeDeWWeLDLeeWW 8.533334 eD9peD9p9Dep9De 15 32 9pe9eD9peD9p9Dep9De9p9eD9pe99e99Dee9 8.533334 eD9leD9l9Del9De 15 32 9e9eD9leD9l9Del9De9l9leD9e99e99Dee9 8.533334 eD9ZeD9Z9DeZ9De 15 34 9Ze9eD9ZeD9Z9DeZ9De9Z9eD9Ze99Ze99DeeZ9 8.533334 eD9WeD9W9DeW9De 15 35 9We9eD9WeD9W9DeW9De99WeD9eW99We99DeeW9W 8.533334 eD9OeD9O9DeO9De 15 33 9Oe9eD9OeD9O9DeO9De99OeD9e99Oe99DeeO9 8.533334 eD5peD5p5Dep5De 15 28 peeD5peD5p5Dep5De55peDpe5eDee5 8.533334 eD5ZeD5Z5DeZ5De 15 30 ZeeD5ZeD5Z5DeZ5De55ZeDZe5ZeDee5Z 8.533334 eD5WeD5W5DeW5De 15 31 WeeD5WeD5W5DeW5De55WeDeW5WeDee5WW 8.533334 eD5OeD5O5DeO5De 15 29 OeeD5OeD5O5DeO5De55OeDeO5eDee5O 8.533334 eD)peD)p)Dep)De 15 28 peeD)peD)p)Dep)De))peD)peeDee) 8.533334 eD)ZeD)Z)DeZ)De 15 30 ZeeD)ZeD)Z)DeZ)De))ZeD)ZeZeDeeZ) 8.533334 eD)OeD)O)DeO)De 15 29 OeeD)OeD)O)DeO)De))OeD)eOeDeeO) 8.533334 e9Lpe9LpL9epL9e 15 34 9pe9e9Lpe9LpL9epL9eL9Lp9e9pe99e9L9Lee9 8.533334 e9LZe9LZL9eZL9e 15 36 9Ze9e9LZe9LZL9eZL9eL9LZ9e9Ze99Ze9L9LeeZ9 8.533334 e9LWe9LWL9eWL9e 15 37 9We9e9LWe9LWL9eWL9eL9L9We9eW99We9L9LeeW9W 8.533334 dD6(dD6(6Dd(6Dd 15 21 6D(dD6(dD6(6Dd(6DdDdd666 8.533334 ZHELZHELEHZLEHZ 15 33 ZHELZHELEHZLEHZLHLEHLZEZZELHLZEEH 8.533334 ZH#LZH#L#HZL#HZ 15 34 ZH#LZH#L#HZL#HZLHLHLZ#Z##Z#LHL##ZH 8.533334 YD6(YD6(6DY(6DY 15 21 Y6YYYD(YD6(YD6(6DY(6DYYYD666 8.533334 OWr=OWr=rWO=rWO 15 23 O==WOrWOWr=OWr=rWO=rWOW=OrWrW= 8.533334 GD6OGD6O6DGO6DG 15 23 OG6DOGD6OGD6O6DGO6DGOGD6OG66 8.533334 GD6(GD6(6DG(6DG 15 21 G6D(GD6(GD6(6DG(6DGGD6G66 8.533334 EW+OEW+O+WEO+WE 15 17 OW+OEW+EOEW+EOW+EW+OEW+O+WEO+WEWE 8.533334 D9LpD9LpL9DpL9D 15 31 9p9D9LpD9LpL9DpL9DL9Lp9D9p999L9DL9 8.533334 D9LZD9LZL9DZL9D 15 33 9Z9D9LZD9LZL9DZL9DL9LZ9D9Z99Z9L9DLZ9 8.533334 D9LWD9LWL9DWL9D 15 34 9W9D9LWD9LWL9DWL9DL9L9WD9W99W9L9DLW9W 8.533334 @D6O@D6O6D@O6D@ 15 22 O6@DO@D6O@D6O6D@O6D@OD6O@66 8.533334 @D6(@D6(6D@(6D@ 15 20 6@D(@D6(@D6(6D@(6D@D6@66 8.533334 6W+O6W+O+W6O+W6 15 17 OW+6OW+6OW+6OW+6W+O6W+O+W6O+W6W6 8.533334 /^p(/^p(p^/(p^/ 15 17 //p^(/^p(/^p(p^/(p^/p^ 8.533334 /^ZK/^ZKZ^/KZ^/ 15 20 /Z/K^/^ZK/^ZKZ^/KZ^/Z^ZKZ 8.533334 /^W(/^W(W^/(W^/ 15 20 //W^(/^W(/^W(W^/(W^/W^WWW 8.533334 /^+(/^+(+^/(+^/ 15 19 //+^(/^+(/^+(+^/(+^/++^+ 8.533334 /D6(/D6(6D/(6D/ 15 19 //6D(/D6(/D6(6D/(6D/D666 8.0 eD9LeD9LL9DeL9De 16 35 9e9eD9LeD9LL9DeL9DeL9L9eD9e99e9L9DLee9 8.0 eD9EeD9EE9DeE9De 16 36 9e9eD9EeD9EE9DeE9DeE99eDE9e99eE99DeeE9E 8.0 eD5EeD5EE5DeE5De 16 32 eeD5EeD5EE5DeE5De5E5eDEe5eEDee5EE 8.0 eD)EeD)EE)DeE)De 16 32 eeD)EeD)EE)DeE)De)E)eD)EeeEDeeEE) 7.529412 BZ)rBZ)r)r)ZBr)ZB 17 25 ZBB)BZr)BBBZ)rBZ)r)r)ZBr)ZBBZBZrBr) 7.529412 #Z)r#Z)r)r)Z#r)Z# 17 26 Z)#Zr)##Z)r#Z)r)r)Z#r)Z##Z###Zrr)And L=3:
24.923077 lINIlINIlINIl 13 20 INlINIlINIlINIlNlINIII 24.923077 l8K8l8K8l8K8l 13 17 Kl8K8l8K8l8K8ll8K8 24.923077 l8G8l8G8l8G8l 13 19 Gl8G8l8G8l8G8llG8GG8 24.923077 O8K8O8K8O8K8O 13 18 OKO8K8O8K8O8K8O8OKO8 24.923077 O8G8O8G8O8G8O 13 20 OGO8G8O8G8O8G8OG8OGOG8 24.923077 /EKE/EKE/EKE/ 13 17 //K/EKE/EKE/EKE/KEEE 24.923077 /E(E/E(E/E(E/ 13 16 //(/E(E/E(E/E(E/EEE 24.923077 (8K8(8K8(8K8( 13 16 K(8K8(8K8(8K8(8K8 24.923077 (8G8(8G8(8G8( 13 18 G(8G8(8G8(8G8(G8GG8 14.294118 OpDOpDOpDpODpODpO 17 19 OpDOpDOpDpODpODpODO 14.294118 Op6Op6Op6pO6pO6pO 17 21 Op6Op6Op6pO6pO6pO6O66 14.294118 )LH)LH)LHL)HL)HL) 17 23 H)LH)LH)LHL)HL)HL))LHLH) 12.0 tk(kttk(kt 10 14 kkt(k(tk(kttk(ktkttk 12.0 r9p9rr9p9r 10 19 9p99rp9pr9p9rr9p9r9p9999rr9 12.0 r9l9rr9l9r 10 19 999lr9lr9l9rr9l9rl99999rr9 12.0 r9Z9rr9Z9r 10 21 9Z99Zr9Zr9Z9rr9Z9r9Z99Z99Zrr9 12.0 r9(9rr9(9r 10 18 99(9r9(r9(9rr9(9r99999rr9 12.0 qc@cqqc@cq 10 16 @qqq@qqq@qcqqc@cqqc@cqqqc@qq 12.0 kVVkkVVk 10 15 kVkkVkkVVkkVVkVVVk 12.0 kVWVkkVWVk 10 18 kWVkkVWkWkVWVkkVWVkVWWVWVWk 12.0 kV+VkkV+Vk 10 17 kV+kkV+k+kV+VkkV+VkV++V+Vk 12.0 eN!NeeN!Ne 10 17 e!eNeN!NeeN!NeNee!!ee 12.0 eM!MeeM!Me 10 18 e!eMMeM!MeeM!MeMee!!eeM 12.0 PMMP\PMMP 12 19 PPMPMPMMP\PMMPPMPPPM 12.0 P!P\P!P 10 17 PP!PP!P\P!PPP!!PP 12.0 M!M\M!M 10 15 !MMM!M\M!MM!!M 12.0 X^kk^XX^kk^X 12 23 kX^kk^XX^kk^Xkk^kX^XXXXk 12.0 XW!WXXW!WX 10 23 XW!WXXW!WX!WXWW!XX!XWXW 12.0 WPrPWWPrPW 10 12 PWPPrWPWrPWrPrPWPrPWWPrPWrW 12.0 WPIPWWPIPW 10 13 PWPIPWIIPIWPWIIPIPWPIPWWPIPWWII 12.0 VPrPVVPrPV 10 11 PVPPrVPrPVrPVrPVVPrPVVPrPVr 12.0 VPIPVVPIPV 10 12 PVPIPVIIPIPVIIPVIPVVPIPVVPIPVII 12.0 UM8U8MUUM8U8MU 14 14 UMUUM888MU8MUM8U8MUUM8U8MU 12.0 UHtHUUHtHU 10 21 UHUtUHtHUUHtHUtHUtUUtHtHU 12.0 UHVHUUHVHU 10 23 UVHUUHVHUUHVHUVHUVVUVUVHVHU 12.0 UHOHUUHOHU 10 20 UOHUOUHOHUUHOHUHUOUOUHOHU 12.0 TcFcTTcFcT 10 16 FTFTcFcTTcFcTcTFFcT 12.0 PMKMPPMKMP 10 17 PPKMPMKPMKMPPMKMPPMPKPPM 12.0 PM!MPPM!MP 10 18 PP!MPMPM!MPPM!MPPMP!!PPM 12.0 P=EPE=PP=EPE=P 14 18 P==PPEEPEP=EPE=PP=EPE=PPEE= 12.0 OcFcOOcFcO 10 15 OFOFOcFcOOcFcOcFOFc 12.0 OTKTOOTKTO 10 11 OKTOKOTKOTKTOOTKTOT 12.0 OP!POOP!PO 10 22 POP!POOP!POP!POPPO!!POP 12.0 NUpUNNUpUN 10 13 UpUNUpNUpNUpUNNUpUNpUU 12.0 NU^UNNU^UN 10 13 U^UNU^NU^NU^UNNU^UNU^U 12.0 NUUNNUUN 10 13 UUNUNUNUUNNUUNUU 12.0 NUWUNNUWUN 10 16 UWUNUWNUWNUWUNNUWUNWUWWWU 12.0 NUTUNNUTUN 10 15 UUTNUNTUNUTUNNUTUNTUTTU 12.0 NUOUNNUOUN 10 14 UOUNOUNOUNUOUNNUOUNOUOU 12.0 NU+UNNU+UN 10 15 U+UNU+NU+NU+UNNU+UN+U++U 12.0 MPpPMMPpPM 10 15 PpPMPMpPMpMPpPMMPpPMPpPPM 12.0 MPWPMMPWPM 10 18 PWPMPMWPMWMPWPMMPWPMPWWPPWWM 12.0 MPTPMMPTPM 10 17 PPMTPMTPMMPTPMMPTPMPTTPTPM 12.0 MPOPMMPOPM 10 16 POPMPOMOPMMPOPMMPOPMPOPOPM 12.0 MHtHMMHtHM 10 20 HMtMHtHMMHtHMtHMtMtHtHM 12.0 MHlHMMHlHM 10 18 HMlMHlHMMHlHMHMllMHHM 12.0 MHVHMMHVHM 10 22 VHMMHVHMMHVHMVHMVVMVVHVHM 12.0 MHOHMMHOHM 10 19 OHMOMHOHMMHOHMHMOMOHOHM 12.0 M8K8MM8K8M 10 10 KMM8K88MK8MM8K8MM8K8M 12.0 KeFeKKeFeK 10 19 eFKeFeKKeFeKeeFeKFeeF 12.0 KDFDKKDFDK 10 16 FKDFDKKDFDKDFKFDF 12.0 K9F9KK9F9K 10 22 9F9K9F9KK9F9K999F99K9F9F9 12.0 G^kk^GG^kk^G 12 21 kG^kk^GG^kk^Gkk^Gk^GGk 12.0 G@kk@GG@kk@G 12 21 kG@kk@GG@kk@GkkGk@GG@k 12.0 G@ee@GG@ee@G 12 22 eG@ee@GG@ee@GeGe@eGeeG@ 12.0 G@^^@GG@^^@G 12 19 G@^^@GG@^^@G^G@^GG@ 12.0 G@!@GG@!@G 10 18 G@!@GG@!@G!G@G!!G@ 12.0 DM!MDDM!MD 10 15 !MDMDM!MDDM!MDM!D!M 12.0 @eVe@@eVe@ 10 23 Ve@eVe@@eVe@VVVeVe@Veee@V 12.0 @eFe@@eFe@ 10 20 eF@eFe@@eFe@eeF@eFeeF@ 12.0 @^kk^@@^kk^@ 12 20 k@^kk^@@^kk^@kk^k@^@k 12.0 =E@E==E@E= 10 14 ==@E@E@E=E@E==E@E=@EE= 12.0 =E/E==E/E= 10 13 //==/EE/E=E/E==E/E=EE= 12.0 8ece88ece8 10 17 eee888c8ece88ece8cceeec8 12.0 8M^M88M^M8 10 13 M^^M888M^8M^M88M^M8^8M 12.0 8MTM88MTM8 10 15 MTM888TM8MTM88MTM8TTT8M 12.0 8MOM88MOM8 10 14 OMOM88O8M8MOM88MOM8OO8M 12.0 8M(M88M(M8 10 12 M(M88(8M8M(M88M(M88M 12.0 6MKM66MKM6 10 16 6KMMK6MKM66MKM6MK666M 12.0 6M!M66M!M6 10 17 6!MM6M!M66M!M6M!!666M 12.0 +PMMP++PMMP+ 12 21 P+PMPM+PMMP++PMMP+PMP++P+PM 12.0 +P!P++P!P+ 10 19 P+P!P+P!P++P!P+PP++!!P+P 12.0 +M!M++M!M+ 10 17 +!MM+M!M++M!M+M++!!+M 11.294118 9P(9P9(P9P(9P9(P9 17 27 9P9P(9P9(P9P(9P9(P9P9P9999PP9 11.076923 kNUkUNkNUkUNk 13 16 UkUkNUkNUkNUkUNkNUkUNkUUk 11.076923 kMPkPMkMPkPMk 13 18 PkPMkPkMPMkMPkPMkMPkPMkPPPMk 11.076923 ^Ol^lO^Ol^lO^ 13 17 O^Ol^lO^Ol^lO^lO^O 11.076923 ZOTZTOZOTZTOZ 13 14 ZOTOZOTZZOTZTOZOTZTOZT 11.076923 ZKDZDKZKDZDKZ 13 19 ZKDZDKZKDZDKZDZZKDZ 11.076923 Ur9U9rUr9U9rU 13 23 9U9U9Ur9Ur9U9rUr9U9rU999U99rr9U 11.076923 P^kPk^P^kPk^P 13 24 PkP^kPk^P^kPk^PkPkP^kP^PPk 11.076923 P@^P^@P@^P^@P 13 22 PP@^P^@P@^P^@PPP^P@^P@P 11.076923 OX^O^XOX^O^XO 13 22 OX^O^XOX^O^XO^XO^XXOXX 11.076923 OXDODXOXDODXO 13 22 OXDODXOXDODXODXOXXDOXX 11.076923 OX6O6XOX6O6XO 13 24 OX6O6XOX6O6XO6XOXX6OX6X6 11.076923 OKDODKOKDODKO 13 18 OKDODKOKDODKODOKDO 11.076923 OG^O^GOG^O^GO 13 20 OG^O^GOG^O^GO^GO^GOG 11.076923 OG@O@GOG@O@GO 13 20 OG@O@GOG@O@GOG@OGOG@ 11.076923 O@^O^@O@^O^@O 13 19 O@^O^@O@^O^@O^@O^O@ 11.076923 Nr9N9rNr9N9rN 13 21 99N9r9Nr9N9rNr9N9rN99999rr9And smokie, the algorithm finds much higher-scoring palindromic cycles in your test cipher:
L=4:140.10811 #O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O%D%O# 37 39 #O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O%D%O#O% 100.0 1LTGTL11LTGTL11LTGTL11LTGTL11LTGTL1 35 37 1LTGTL11LTGTL11LTGTL11LTGTL11LTGTL11L 97.22222 |1LTTL1|1LTTL1|1LTTL1|1LTTL1|1LTTL1| 36 38 |1LTTL1|1LTTL1|1LTTL1|1LTTL1|1LTTL1|1L 96.77419 |LTGTL|LTGTL|LTGTL|LTGTL|LTGTL| 31 32 |LTGTL|LTGTL|LTGTL|LTGTL|LTGTL|L 96.77419 |1TGT1|1TGT1|1TGT1|1TGT1|1TGT1| 31 32 |1TGT1|1TGT1|1TGT1|1TGT1|1TGT1|1 96.77419 |1LGL1|1LGL1|1LGL1|1LGL1|1LGL1| 31 33 |1LGL1|1LGL1|1LGL1|1LGL1|1LGL1|1L 61.44 5F&4&F5F&4&F5F&4&F5F&4&F5 25 28 5F&4&F5F&4&F5F&4&F5F&4&F5F&4 61.44 .<*K*<.<*K*<.<*K*<.<*K*<. 25 28 .<*K*<.<*K*<.<*K*<.<*K*<.<*K 36.0 1LT5TL11LT5TL11LT5TL1 21 37 1LT5TL11LT5TL11LT5TL115LT5TL11LTTL11L 34.105263 |LT5TL|LT5TL|LT5TL| 19 32 |LT5TL|LT5TL|LT5TL|5LT5TL|LTTL|L 34.105263 |1T5T1|1T5T1|1T5T1| 19 32 |1T5T1|1T5T1|1T5T1|15T5T1|1TT1|1 34.105263 |1L_L1|1L_L1|1L_L1| 19 32 |1L_L1|1L_L1|1L_L1|1LL1|1LL1|1_L 34.105263 |1L5L1|1L5L1|1L5L1| 19 33 |1L5L1|1L5L1|1L5L1|15L5L1|1LL1|1L 34.105263 y:cMc:y:cMc:y:cMc:y 19 21 y:cMc:y:cMc:y:cMc:y:c 34.105263 cLTGTLcLTGTLcLTGTLc 19 20 LTGTccLLTGcTLcLTGTLcLTGTLcLTGTLcL 34.105263 _9tjt9_9tjt9_9tjt9_ 19 19 _9tjt9_9tjt9_9tjt9_ 34.105263 _9tMt9_9tMt9_9tMt9_ 19 19 _9tMt9_9tMt9_9tMt9_ 34.105263 UZzyzZUZzyzZUZzyzZU 19 19 yUZzyzZUZzyzZUZzyzZU 34.105263 UZzJzZUZzJzZUZzJzZU 19 19 UZzJzZUZzJzZUZzJzZU 34.105263 UZz>zZUZz>zZUZz>zZU 19 19 UZz>zZUZz>zZUZz>zZU 34.105263 HER>REHER>REHER>REH 19 21 HER>REHER>REHER>REHER 34.105263 5F&|&F5F&|&F5F&|&F5 19 28 |5F&|&F5F&|&F5F&|&F5F&&F5|F&| 34.105263 4&FcF&4&FcF&4&FcF&4 19 26 Fc&c4&FcF&4&FcF&4&FcF&4&FcF&c4 16.0 |zZdZz||zZdZz| 14 17 |Zzd|zZdZz||zZdZz|zZ| 16.0 |zZUZz||zZUZz| 14 18 |UZz|zZUZz||zZUZz|zZ|U 16.0 |z*K*z||z*K*z| 14 21 |*Kz*|z*K*z||z*K*z|*K*z|*K 16.0 |REHER||REHER| 14 20 |HER|REHER||REHER|REHE|R 16.0 fzZdZzffzZdZzf 14 17 ZfzdffzZdZzffzZdZzfzZf 16.0 fzZUZzffzZUZzf 14 18 UZfzffzZUZzffzZUZzfzZfU 16.0 Zz:y:zZZz:y:zZ 14 14 yZ:z:yz:ZZz:y:zZZz:y:zZ 16.0 Zz:q:zZZz:q:zZ 14 14 Z:z:z:ZZz:q:zZZz:q:zZ 16.0 Zz:V:zZZz:V:zZ 14 15 ZV:z:z:ZZz:V:zZZz:V:zZV 16.0 Zz:>:zZZz:>:zZ 14 14 Z:z:>z:ZZz:>:zZZz:>:zZ 16.0 Zz(y(zZZz(y(zZ 14 22 yZz(y(zZZz(y(zZ(Z(zy(zZ 16.0 Zz(_(zZZz(_(zZ 14 22 _Zz(_(zZZz(_(zZ(Z(z(zZ_ 16.0 Zz(J(zZZz(J(zZ 14 22 Zz(J(zZZz(J(zZ(Z(z(JzZ 16.0 Zz(.(zZZz(.(zZ 14 23 .Zz(.(zZZz(.(zZ(Z(z.(.zZ 16.0 TL|LTjTL|LTTL|LTjTL|LT 22 26 |LTjTL|LTjTL|LTTL|LTjTL|LTTL|L 16.0 TL|LTHTL|LTTL|LTHTL|LT 22 27 |LTHTL|LTHTL|LTTL|LTHTL|LTTHL|L 16.0 TL1J1LTTL1J1LT 14 32 1LTTL1J1LTTL1J1LTTL11LTTL11LTJTL11L 16.0 TL1>1LTTL1>1LT 14 19 1LTTL11>LTTL11LTTL1>1LTTL1>1LTTL11L 16.0 TL181LTTL181LT 14 36 1LT8TL181LTTL181LTTL1818LT8TL181LTTL11L8 16.0 TL141LTTL141LT 14 27 1LTTL411LTTL141LTTL141LT4TL11LTTL11L4 16.0 T1|1TjT1|1TT1|1TjT1|1T 22 26 |1TjT1|1TjT1|1TT1|1TjT1|1TT1|1 16.0 T1|1THT1|1TT1|1THT1|1T 22 27 |1THT1|1THT1|1TT1|1THT1|1TTH1|1 16.0 RLTGTLRRLTGTLR 14 15 LTGTRLLRTGRTLLTGTLRLTGTLRRLTGTLRL 16.0 RLT;TLRRLT;TLR 14 16 LTT;RLLRTRTLLTTLRLT;TLRRLT;TLRL; 16.0 OF&|&FOOF&|&FO 14 27 O|OFO&O|&FOF&|&FOOF&|&FOF&&OFOO|FO&O| 16.0 OF&4&FOOF&4&FO 14 27 OOFO&O4&FOF&4&FOOF&4&FOF&4&OFOOFO&O4 16.0 OF&(&FOOF&(&FO 14 28 OOFO&(O&F(OF&(&FOOF&(&FOF(&&OF(OOF(O&O 16.0 O%D%OlO%D%OO%D%OlO%D%O 22 31 O%D%OO%D%OlO%D%OO%D%OlO%D%OlO%D%OOl% 16.0 O%D%OVO%D%OO%D%OVO%D%O 22 36 O%D%OVO%D%OO%D%OVO%D%OO%D%OOV%D%OOV% 16.0 O%D%OSO%D%OO%D%OSO%D%O 22 24 O%DS%OO%D%OO%D%OSO%D%OO%D%OSO%D%OO% 16.0 LTGTLSLTGTLLTGTLSLTGTL 22 23 SLTGTLLTGTLSLTGTLLTGTLSLTGTLL 16.0 LTGTL>LTGTLLTGTL>LTGTL 22 29 LTGTL>LTGTLLTGTL>LTGTL>LTGTLL 16.0 LTGTL.LTGTLLTGTL.LTGTL 22 24 .LTGT.LLTGTL.LTGTLLTGTL.LTGTL.L 16.0 L1|1LqL1|1LL1|1LqL1|1L 22 22 |1LL1|1LL1|1LqL1|1LL1|1LqL1|1L 16.0 L1|1LjL1|1LL1|1LjL1|1L 22 27 |1LjL1|1LjL1|1LL1|1LjL1|1LL1|1L 16.0 L1|1LML1|1LL1|1LML1|1L 22 27 |1LML1|1LML1|1LL1|1LML1|1LL1|1L 16.0 L1|1LKL1|1LL1|1LKL1|1L 22 29 |1KLL1|1LKL1|1LL1|1LKL1|1LKL1|1LK 16.0 L1|1LHL1|1LL1|1LHL1|1L 22 28 |1LHL1|1LHL1|1LL1|1LHL1|1LHL1|1L 16.0 F&4&FUF&4&FF&4&FUF&4&F 22 26 UF&4&FUF&4&FF&4&FUF&4&FF&U4 16.0 :c*K*c::c*K*c: 14 21 *K:c*c::c*K*c::c*K*c:*K*:c*K 16.0 :O%D%O::O%D%O: 14 34 O%D%O:O%D%O::O%D%O:O%:D%OO%D%O:O%D%O:O% 16.0 9t%D%t99t%D%t9 14 28 %D%9t%D%t99t%D%t9%D9%t%D%%D%t9% 16.0 3F&4&F33F&4&F3 14 18 F&43&F3F&4&F3F&4&F33F&4&F33F&4 16.0 1|1ZdZ1|11|1ZdZ1|1 18 22 |1Zd1|1ZdZ1|11|1ZdZ1|11Z|1 16.0 1|1ZUZ1|11|1ZUZ1|1 18 23 |1UZ1|1ZUZ1|11|1ZUZ1|11Z|1U 16.0 1|1*K*1|11|1*K*1|1 18 26 |*1K*1|1*K*1|11|1*K*1|1*K*1|1*K 16.0 1LfjfL11LfjfL1 14 32 1LfjfL11LfjfL1f1LL11LjL11LfL1f1L 16.0 1LfdfL11LfdfL1 14 32 1LfdfL11LfdfL1f1LL11dLL11LfL1f1L 16.0 1LTjTL11LTjTL1 14 35 1LTjTL11LTjTL11LTTL11LTjTL11LTTL11L 16.0 1LTHTL11LTHTL1 14 36 1LTHTL11LTHTL11LTTL11LTHTL11LTTHL11L 16.0 1LT;TL11LT;TL1 14 17 1LTT;L11LTTL11LTTL11LT;TL11LT;TL11L; 16.0 1LT:TL11LT:TL1 14 31 1LT:TL:11LT:TL11LT:TL1:1LTTL1:1LTTL:11L 16.0 *c:y:c**c:y:c* 14 23 *y:c*c:y:c**c:y:c**c:y**:c* 16.0 *c:_:c**c:_:c* 14 23 *_:c*c:_:c**c:_:c**c:**:c_* 16.0 *c:>:c**c:>:c* 14 23 *:c*c:>:c**c:>:c**c:>**:c* 16.0 *L1|1L**L1|1L* 14 14 |*1L*L1|1L**L1|1LL1|1*L*L1|1L**L1|1L* 16.0 *L1l1L**L1l1L* 14 14 *1L*L1l1L**L11LL11*Ll*L1l1L**L1l1L* 16.0 *L1c1L**L1c1L* 14 14 *1Lc*cL11Lc**L1c1LL11c*L*L1c1L**L1c1L* 16.0 %L1|1L%%L1|1L% 14 35 |%1L%%%L1|1L%%L1|1L%L1|1%L%%L1|1%L%L1|1L% 16.0 %L1J1L%%L1J1L% 14 33 %1L%%%L1J1L%%L1J1L%L11%L%%L11%L%JL11L% 16.0 %L181L%%L181L% 14 37 %1L%8%%L181L%%L181L%L1818%L8%%L181%L%L11L%8 15.304348 pF&4&FF&4&FpF&4&FF&4&Fp 23 27 pF&4&FF&4&FpF&4&FF&4&FpFp&4 15.304348 VF&4&FF&4&FVF&4&FF&4&FV 23 27 VF&4&FF&4&FVF&4&FF&4&FVF&V4 15.304348 SF&4&FF&4&FSF&4&FF&4&FS 23 26 SF&4&FF&4&FSF&4&FF&4&FSF&4 15.304348 /LTGTLLTGTL/LTGTLLTGTL/ 23 24 LT/G/TL/LTGTLLTGTL/LTGTLLTGTL/L 15.238095 pF&&FUF&&FpF&&FUF&&Fp 21 25 UpF&&FUF&&FpF&&FUF&&FpFp&U 15.238095 VF&&FUF&&FVF&&FUF&&FV 21 25 UVF&&FUF&&FVF&&FUF&&FVF&VU 15.238095 SLTTL>LTTLSLTTL>LTTLS 21 27 SLTTL>LTTLSLTTL>LTTLS>LTTLL 15.238095 KV<.<K<.<VKV<.<K<.<VK 21 21 .<KV<.<K<.<VKV<.<K<.<VK 15.238095 /LTTLSLTTL/LTTLSLTTL/ 21 22 SLT//TL/LTTLSLTTL/LTTLSLTTL/L 15.058824 tfzZtZzftfzZtZzft 17 20 tZfzftfzZtZzftfzZtZzftzZf 15.058824 pF4FUF4FpF4FUF4Fp 17 21 UpF4FUF4FpF4FUF4FpFpU4 15.058824 p&4&l&4&p&4&l&4&p 17 22 p&4&l&4&p&4&l&4&plp&l4 15.058824 p&4&U&4&p&4&U&4&p 17 21 Up&4&U&4&p&4&U&4&pp&U4 15.058824 Y*G2*2G*Y*G2*2G*Y 17 21 Y*G2*2G*Y*G2*2G*Y**G* 15.058824 VF4FUF4FVF4FUF4FV 17 21 UVF4FUF4FVF4FUF4FVFVU4 15.058824 V&4&^&4&V&4&^&4&V 17 21 ^V&4&^&4&V&4&^&4&V^&V4L=3:
108.0 O%D%OO%D%OO%D%OO%D%OO%D%OO%D%O 30 32 O%D%OO%D%OO%D%OO%D%OO%D%OO%D%OO% 108.0 %O#O%%O#O%%O#O%%O#O%%O#O%%O#O% 30 30 #O%%O#O%%O#O%%O#O%%O#O%%O#O%%O#O% 103.68 #ODO#ODO#ODO#ODO#ODO#ODO# 25 26 #ODO#ODO#ODO#ODO#ODO#ODO#O 103.68 #%D%#%D%#%D%#%D%#%D%#%D%# 25 26 #%D%#%D%#%D%#%D%#%D%#%D%#% 75.0 LTGTLLTGTLLTGTLLTGTLLTGTL 25 26 LTGTLLTGTLLTGTLLTGTLLTGTLL 75.0 L1|1LL1|1LL1|1LL1|1LL1|1L 25 25 |1LL1|1LL1|1LL1|1LL1|1LL1|1L 75.0 1TGT11TGT11TGT11TGT11TGT1 25 26 1TGT11TGT11TGT11TGT11TGT11 75.0 1LTTL11LTTL11LTTL11LTTL11LTTL1 30 32 1LTTL11LTTL11LTTL11LTTL11LTTL11L 75.0 1LGL11LGL11LGL11LGL11LGL1 25 27 1LGL11LGL11LGL11LGL11LGL11L 72.11538 |LTTL|LTTL|LTTL|LTTL|LTTL| 26 27 |LTTL|LTTL|LTTL|LTTL|LTTL|L 72.11538 |1TT1|1TT1|1TT1|1TT1|1TT1| 26 27 |1TT1|1TT1|1TT1|1TT1|1TT1|1 71.42857 |TGT|TGT|TGT|TGT|TGT| 21 21 |TGT|TGT|TGT|TGT|TGT| 71.42857 |LGL|LGL|LGL|LGL|LGL| 21 22 |LGL|LGL|LGL|LGL|LGL|L 71.42857 |1G1|1G1|1G1|1G1|1G1| 21 22 |1G1|1G1|1G1|1G1|1G1|1 48.0 F&4&FF&4&FF&4&FF&4&F 20 23 F&4&FF&4&FF&4&FF&4&FF&4 48.0 <*K*<<*K*<<*K*<<*K*< 20 23 <*K*<<*K*<<*K*<<*K*<<*K 48.0 *<.<**<.<**<.<**<.<* 20 20 .<**<.<**<.<**<.<**<.<* 48.0 &FcF&&FcF&&FcF&&FcF& 20 21 Fc&c&FcF&&FcF&&FcF&&FcF&c 48.0 &F5F&&F5F&&F5F&&F5F& 20 20 5F&&F5F&&F5F&&F5F&&F5F& 45.17647 5F4F5F4F5F4F5F4F5 17 19 5F4F5F4F5F4F5F4F5F4 45.17647 5&4&5&4&5&4&5&4&5 17 19 5&4&5&4&5&4&5&4&5&4 45.17647 .<K<.<K<.<K<.<K<. 17 19 .<K<.<K<.<K<.<K<.<K 45.17647 .*K*.*K*.*K*.*K*. 17 19 .*K*.*K*.*K*.*K*.*K 27.0 c:y:cc:y:cc:y:c 15 15 y:cc:y:cc:y:cc:y:c 27.0 c:>:cc:>:cc:>:c 15 15 :cc:>:cc:>:cc:>:c 27.0 ZzyzZZzyzZZzyzZ 15 15 yZzyzZZzyzZZzyzZ 27.0 ZzJzZZzJzZZzJzZ 15 15 ZzJzZZzJzZZzJzZ 27.0 Zz>zZZz>zZZz>zZ 15 15 Zz>zZZz>zZZz>zZ 27.0 TLcLTTLcLTTLcLT 15 19 LTTccLLTcTLcLTTLcLTTLcLTTLcL 27.0 TL4LTTL4LTTL4LT 15 24 LTTL4LTTL4LTTL4LT4TLLTTLL4 27.0 T&|&TT&|&TT&|&T 15 23 |TT&|&TT&|&TT&|&T&&T|TT&| 27.0 T&4&TT&4&TT&4&T 15 23 TT&4&TT&4&TT&4&T&4&TTT&4 27.0 REHERREHERREHER 15 15 HERREHERREHERREHER 27.0 LT5TLLT5TLLT5TL 15 26 LT5TLLT5TLLT5TL5LT5TLLTTLL 27.0 F&|&FF&|&FF&|&F 15 23 |F&|&FF&|&FF&|&FF&&F|F&| 27.0 ER>REER>REER>RE 15 17 ER>REER>REER>REER 27.0 :cMc::cMc::cMc: 15 17 :cMc::cMc::cMc::c 27.0 9tjt99tjt99tjt9 15 15 9tjt99tjt99tjt9 27.0 9tMt99tMt99tMt9 15 15 9tMt99tMt99tMt9 27.0 1T5T11T5T11T5T1 15 26 1T5T11T5T11T5T115T5T11TT11 27.0 1L_L11L_L11L_L1 15 26 1L_L11L_L11L_L11LL11LL11_L 27.0 1L5L11L5L11L5L1 15 27 1L5L11L5L11L5L115L5L11LL11L 27.0 %D%V%D%%D%V%D%%D%V%D% 21 23 %D%V%D%%D%V%D%%D%V%D%V% 25.578949 OTLOLTOTLOLTOTLOLTO 19 30 OLTOOTLOLTOTLOLTOTLOLTOTOLOLTTLOOL 25.3125 _9tt9_9tt9_9tt9_ 16 16 _9tt9_9tt9_9tt9_ 25.3125 UZzzZUZzzZUZzzZU 16 16 UZzzZUZzzZUZzzZU 24.923077 |T5T|T5T|T5T| 13 21 |T5T|T5T|T5T|5T5T|TT| 24.923077 |L_L|L_L|L_L| 13 21 |L_L|L_L|L_L|LL|LL|_L 24.923077 |L5L|L5L|L5L| 13 22 |L5L|L5L|L5L|5L5L|LL|L 24.923077 |1p1|1p1|1p1| 13 14 |1p1|11|1p1|1p1|1p1|1 24.923077 |1_1|1_1|1_1| 13 21 |1_1|1_1|1_1|11|11|1_ 24.923077 |151|151|151| 13 22 |151|151|151|1551|11|1 24.923077 ycMcycMcycMcy 13 14 ycMcycMcycMcyc 24.923077 y:j:y:j:y:j:y 13 14 y:j:y:j:y:j:y: 24.923077 y:d:y:d:y:d:y 13 14 y:d:y:d:y:d:y: 24.923077 y:M:y:M:y:M:y 13 14 y:M:y:M:y:M:y: 24.923077 cTGTcTGTcTGTc 13 13 TGTccTGcTcTGTcTGTcTGTc 24.923077 cLGLcLGLcLGLc 13 14 LGccLLGcLcLGLcLGLcLGLcL 24.923077 _tjt_tjt_tjt_ 13 13 _tjt_tjt_tjt_ 24.923077 _tMt_tMt_tMt_ 13 13 _tMt_tMt_tMt_ 24.923077 _9j9_9j9_9j9_ 13 13 _9j9_9j9_9j9_ 24.923077 _9d9_9d9_9d9_ 13 13 _9d9_9d9_9d9_ 24.923077 _9M9_9M9_9M9_ 13 13 _9M9_9M9_9M9_ 24.923077 _9J9_9J9_9J9_ 13 13 _9J9_9J9_9J9_ 24.923077 UzyzUzyzUzyzU 13 13 yUzyzUzyzUzyzU 24.923077 UzJzUzJzUzJzU 13 13 UzJzUzJzUzJzU 24.923077 Uz>zUz>zUz>zU 13 13 Uz>zUz>zUz>zU 24.923077 UZyZUZyZUZyZU 13 13 yUZyZUZyZUZyZU 24.923077 UZjZUZjZUZjZU 13 13 UZjZUZjZUZjZU 24.923077 UZMZUZMZUZMZU 13 13 UZMZUZMZUZMZU 24.923077 UZJZUZJZUZJZU 13 13 UZJZUZJZUZJZU 24.923077 UZ>ZUZ>ZUZ>ZU 13 13 UZ>ZUZ>ZUZ>ZU 24.923077 K*y*K*y*K*y*K 13 16 *yK*y*K*y*K*y*K**K 24.923077 K*p*K*p*K*p*K 13 13 *Kp**K*p*K*p*K*p*K 24.923077 K*V*K*V*K*V*K 13 13 *KV**K*V*K*V*K*V*K 24.923077 K*C*K*C*K*C*K 13 13 *K**K*C*K*C*K*C*K 24.923077 K*>*K*>*K*>*K 13 16 *K*>*K*>*K*>*K**K 24.923077 HR>RHR>RHR>RH 13 14 HR>RHR>RHR>RHR 24.923077 HEyEHEyEHEyEH 13 14 yHEyEHEyEHEyEHE 24.923077 HE>EHE>EHE>EH 13 14 HE>EHE>EHE>EHE 24.923077 HE.EHE.EHE.EH 13 15 .HE.EHE.EHE.EH.E 24.923077 DTGTDTGTDTGTD 13 21 DTGTDTGTDTGTDTGDTDTGT 24.923077 DT5TDT5TDT5TD 13 21 DT5TDT5TDT5TD5T5DTDTT 24.923077 D%G%D%G%D%G%D 13 19 %DG%%D%G%D%G%D%G%D%%D%G% 24.923077 D%5%D%5%D%5%D 13 23 %D%5%D%5%D%5%D%55%D%%D%% 24.923077 BO#OBO#OBO#OB 13 16 #OOB#OOB#OBBO#OBO#OBO#OBO#O 24.923077 5F|F5F|F5F|F5 13 19 |5F|F5F|F5F|F5FF5|F| 24.923077 5F(F5F(F5F(F5 13 16 5F(F(5F(F5F(F5F(F5(F( 24.923077 5&|&5&|&5&|&5 13 19 |5&|&5&|&5&|&5&&5|&| 24.923077 4FcF4FcF4FcF4 13 18 Fcc4FcF4FcF4FcF4FcFc4 24.923077 4&c&4&c&4&c&4 13 18 c&c4&c&4&c&4&c&4&c&c4 24.923077 .<d<.<d<.<d<. 13 17 .<d<.<d<.<d<.<<.< 24.923077 .<U<.<U<.<U<. 13 18 .<U<.<U<.<U<.<<.<U 24.923077 #OdO#OdO#OdO# 13 20 #OO#OdO#OdO#OdO#OO#OO#O 24.923077 #ONO#ONO#ONO# 13 26 #ONO#ONO#ONO#NONO#OO#OO#NO 12.0 |zjz||zjz| 10 12 |jz|zjz||zjz|z| 12.0 |zdz||zdz| 10 12 |zd|zdz||zdz|z| 12.0 |zZZz||zZZz| 12 15 |Zz|zZZz||zZZz|zZ| 12.0 |zUz||zUz| 10 13 |Uz|zUz||zUz|z|U 12.0 |zKz||zKz| 10 14 |Kz|zKz||zKz|Kz|KSo I think I can conclude from this that Z340 and Z408 do not show strong palindromic cycles in their encoding.
I am still mystified by "+F+FF+++++F++F+".
Sorry I did not have a chance to convert symbols to numbers. Here is the symbolic version of your cipher that I’m using:
#.OW|Y%<*DyNS1U7K LpT^H/_G%5O9tZf-V B2/:#FOj)z8Td-c&( EMW%*<Dc+;%.PNRfL O:4B12J38|t&l1^>/ 9L)Ry#_F(Tfz95kE: +G3Z-tHcO)E<UdR*K FZY%*<jzfT&BDMN+% CLt)14(|fJ9&FB8O. <#cN1@SL3T:VGO5%_ TqLyp1F&|84(>:+1& FDcNbz/38Z^W9U2dX %5BR+O3*F(LlTt&7E 84Z2#&OjFBH5;(GM% PDT%XOK*pL31lz8c# :SE3RkOV|>yPR<.FB 1%(ECLYD<*Tk;%K*p G^J)TfAt<HqL9OX#. <:z&NOC1bZ-)AcEf| l1VR/_LbU-;%*K48A
Thanks a lot for doing that. After looking at the results, I agree that the 340 overall is definitely not palindromic.
I am very interested in the idea that he may have used some creative symmetrical cycles like this one:
H B B H B B B B B B B B H B B H
And will take a closer look at some of the symbols low in count but spread distanced far from the center of the message.
I’m skeptic towards "creative cycling" or "exotic cycling" because it would serve no real purpose, randomization would be more effective.
A cycle like "HBBHBBBBBBBBHBBH" looks interesting but the only requirement is that any symbol would have to repeat twice between the first and second, third and fourth "H". It is the symmetric regionality of the "H" symbol that allows for such things to happen.
There are 3906 two symbol cycles to consider, and some of them will be interesting.
A cycle like "+F+FF+++++F++F++F+FF+++++F++F+" looks interesting but it makes no sense at all. There are factors that at least have to be considered here in the formation of such:
1. The "+" symbol is spread very evenly throughout the cipher and thus by default has more chance to get caught up by other symbols.
2. The frequency of the "+" symbol allows for longer repeats to form.
3. Cyclic homophonic substitution will in general spread out symbols more evenly throughout the cipher, cycles will cycle.
Randomization of the cipher do not equally compare point 1 and 3 so now you have just come up with just another way of measuring the encoding.
I’m skeptic towards "creative cycling" or "exotic cycling" because it would serve no real purpose, randomization would be more effective.
True. But intentionally trying to make more, longer unique sequences would not serve any purpose either, especially if he transposed the plaintext first. If anything, Zodiac was certainly creative.
A cycle like "HBBHBBBBBBBBHBBH" looks interesting but the only requirement is that any symbol would have to repeat twice between the first and second, third and fourth "H". It is the symmetric regionality of the "H" symbol that allows for such things to happen. There are 3906 two symbol cycles to consider, and some of them will be interesting.
Yes you are right. Any time you have a symbol that appears close to the beginning and end of a message then you will get a lot of false creative cycles.
A cycle like "+F+FF+++++F++F++F+FF+++++F++F+" looks interesting but it makes no sense at all. There are factors that at least have to be considered here in the formation of such:
1. The "+" symbol is spread very evenly throughout the cipher and thus by default has more chance to get caught up by other symbols.
2. The frequency of the "+" symbol allows for longer repeats to form.
3. Cyclic homophonic substitution will in general spread out symbols more evenly throughout the cipher, cycles will cycle.
I agree that it does not make any sense, and that the above factors may be exactly why we see +F+FF+++++F++F++F+FF+++++F++F+.
I still think that the more, longer unique sequences were created by some type of mechanism, perhaps very simple, and he was not intentionally thinking about increasing the more, longer unique sequences statistic. I am glad that we have resolved the question of palindromic cycling.
True. But intentionally trying to make more, longer unique sequences would not serve any purpose either, especially if he transposed the plaintext first. If anything, Zodiac was certainly creative.
I’ve been thinking lately, that it is actually the 408 which displays longer unique sequences (24 is most statistically significant). And after removal of the "+" symbol the 340 does not have as many length 17 sequences as before (from 26 to 24). It seems that ‘periodic’ interruption such as the "+" symbol shortens the unique sequences overall but increases the count of the shorter sequences. It horizontally compresses the bell curve and therefore its height increases.
True. But intentionally trying to make more, longer unique sequences would not serve any purpose either, especially if he transposed the plaintext first. If anything, Zodiac was certainly creative.
I’ve been thinking lately, that it is actually the 408 which displays longer unique sequences (24 is most statistically significant). And after removal of the "+" symbol the 340 does not have as many length 17 sequences as before (from 26 to 24). It seems that ‘periodic’ interruption such as the "+" symbol shortens the unique sequences overall but increases the count of the shorter sequences. It horizontally compresses the bell curve and therefore its height increases.
I was unable to quite match your statistic and I included a high count, uniformly distributed, not apparently cyclic symbol in all of the 400 messages. I was in the ballpark with a few but not quite there.
I was unable to quite match your statistic and I included a high count, uniformly distributed, not apparently cyclic symbol in all of the 400 messages. I was in the ballpark with a few but not quite there.
It is strange, in various ways the 340 displays nearly mythical properties.
Something else.
I came up with a hypothetical scenario just to show that a clean shift of a secondary period is possible without overly disturbing the main period. Imagine that in the following image it shows a bigram repeat map with the orange squares being the start position of each period 30 bigram repeat and the red squares the end. Now the only thing that needs to be done to shift period 30 to 29 is remove one of the columns between the bigram repeats. As little as 5 symbols could do it given that the bigram regionality condition is met. Another version of this would be to format the cipher in 30 columns and remove a column then, which will always results in a shift but it diminishes the main period somewhat.
I’m not saying that these things were done in that way but I’m showing it like this to help imagine how it is possible.
