I think Jarlve and smokie have a better sense of what the pivots might signify, since they have been studying so many combinations and variations of transpositions in great detail, particularly with respect to their effects on repeating bigrams. I wonder if the pivots are really related to the unusual peaks in periodic bigrams.
I also still wonder if there’s some classical cipher type that we haven’t fully explored yet that tends to produce pivot-like patterns.
If you consider the following: there are N configurations in which period A bigram repeats can translate into a period B pivot pair. Then, perhaps N is different for combinations of A and B. That doesn’t help with intuition but these things are mechanically complicated to say the least.
Good point. It would be an interesting exercise to precisely map out all those configurations.
Here are the updated stats with more shuffles:
The effect of more frequent pivot pairs at period 4 is no longer as prominent as before. Now period 3 with 80 repeating bigrams produces pivot pairs more often. So, I’m no longer confident that pivot pair production is more likely with specific periods since the differences are not significant.
Here’s the full spreadsheet if you’re curious: https://docs.google.com/spreadsheets/d/ … sp=sharing
The effect of more frequent pivot pairs at period 4 is no longer as prominent as before. Now period 3 with 80 repeating bigrams produces pivot pairs more often. So, I’m no longer confident that pivot pair production is more likely with specific periods since the differences are not significant.
I agree, thanks for running it.
I noticed something interesting. As you can see, there is a repeated sequence of symbols in 2 different lines. But 3 symbols before them, there is the "plus" sign – the same happens in both lines, which could mean a word being repeated, with the "plus" sign possibly being the 1st letter of that word. I red somewhere that in trying to solve symbols, one should remember that many english words end up in "ING".
Those patterns are very interesting; they and others are included in the lists here:
http://zodiackillerciphers.com/wiki/ind … ength:_3_2
I’ve long been intrigued by these questions:
– Do those patterns indicate repetitions in the underlying plaintext? (I think the answer is yes)
– If Z340’s message was manipulated before symbols were assigned, then would reversing the manipulation cause more repeating patterns to appear? (I think the answer is yes, but there are also false manipulations that would produce MORE such patterns)
Do you see any commonalities between this and the bigram r,j, i, Square, Circle.
I noticed something interesting. As you can see, there is a repeated sequence of symbols in 2 different lines. But 3 symbols before them, there is the "plus" sign – the same happens in both lines, which could mean a word being repeated, with the "plus" sign possibly being the 1st letter of that word. I red somewhere that in trying to solve symbols, one should remember that many english words end up in "ING".
I am quoting my last message (please read it to understand my way of thinking) to mention something else I didn’t before. If the repeated sequence of letters (F, B and the backwards C) in 2 different lines could actually mean the same word being repeated, this also could mean that the different letters/symbols that appear after the + sign (in one line, the letters Z, R and the "half-filled O", and on the other line, the N, the I and the "new moon" symbol) could be different cipher letters/symbols that decode to the same letters – for example, the Z and the N would decode to the same letter, while the same happening to both the letters R and I.
Also: the + sign is the most repeated symbol in the 340 cipher. In fact, 3 times in the cipher, 2 + signs are connected to each other. Asuming that the + sign could be the first letter of a word that ends with F, B and the backwards C, I feel that this is a 7 letter word that could end in "ing". In here, you can see the 7 letter words in english that end in "lling" – they are not many: http://www.thefreedictionary.com/words- … n-lling#w7
Excuse me but the reasoning about shuffling the cipher as a deck and the probability you have found just lead to one conclusion: indeed the chance of finding 2-pivots patterns by shuffling the cipher and by analyzing plaintexts (and then use homphonic substitution) is quite the same ( 1 in 240.000 against 1 in 280.000) so the research of 2-pivots pattern is not a good evidence of non-randomness or transpositions at all. At first glance it might be very odd finding these 2 patterns and your own research proves that this double pattern is very uncommon; sadly it happens that this pattern has the same proability of occurrance in random or shuffled texts as well and this fact doesn’t help.
This IOF and FBC section is indeed one of the most interesting parts of the cipher.
QT
*ZODIACHRONOLOGY*
In z340 there are 338 sequences of 3 symbols and the total number of couples of 3 sequences is (335×336)/2 = 56280.
The probability of finding a couple of equal sequences is 1/(60)^3. In a random text the probability of finding 2 equal couples of 3 sequences is:
(1/(60)^3) ^2 x (1 – 1/(60)^3)^56278 x (combinations of 56280 elements in 2) = 2,6 % or 1 chance in 38.
Moreover, tha probability of the pattern + ??? FBc or 3.59E-12 is wrong and this would be the chance of finding such sequence if we had only 1 couple ( or a text of 14 letters only) :there are indeed 56616 couples of sequences of lenght 7 so the chance of having 2 sequence with that pattern is equal to 12% or 1 in 8
