I may make analysis of the pairs a low priority on second thought. We will see. Has anyone ever casted the message into different widths to look at repeats by rows? I am wondering about mirroring and casting into 15 columns. I may do it later today but have to work right now.

Another good exercise would be to just encode a homphonic message by hand to see what it is like to try to not repeat. I like the idea of something simple, like 15 columns and just not repeating by row it seems a lot easier of a rule to follow than the sliding window rule.

We were able to make the distinctive 26 L=17 shape with a palindromic cycle A B C D C B A B C D C B A which makes the A’s and D’s farther apart, but also makes the B distances vary and the C’s closer together. Even though the 340 is not palindromic, I wonder why we were able to make the shape and I wonder if random selection would play a similar role.

For instance, homophone group A B C D. We cycle A B C D A which makes the A’s far apart. But we could make them farther apart by randomly selecting one more B, C or D before we get to that last A and go A B C D C A. That would accomplish the randomness and possibly the shape like the palindromic did.

I may make analysis of the pairs a low priority on second thought. We will see. Has anyone ever casted the message into different widths to look at repeats by rows? I am wondering about mirroring and casting into 15 columns. I may do it later today but have to work right now.

If you are talking about unigram repeats then here is a table:

Normal, Dimension(2,170): 2
Normal, Dimension(3,114): 3
Normal, Dimension(4,85): 4
Normal, Dimension(5,68): 3
Normal, Dimension(6,57): 6
Normal, Dimension(7,49): 6
Normal, Dimension(8,43): 7
Normal, Dimension(9,38): 9
Normal, Dimension(10,34): 7
Normal, Dimension(11,31): 14
Normal, Dimension(12,29): 11
Normal, Dimension(13,27): 14
Normal, Dimension(14,25): 17
Normal, Dimension(15,23): 16
Normal, Dimension(16,22): 17
Normal, Dimension(17,20): 18
Normal, Dimension(18,19): 24
Normal, Dimension(19,18): 24
Normal, Dimension(20,17): 25

Mirror, Dimension(2,170): 2
Mirror, Dimension(3,114): 3
Mirror, Dimension(4,85): 4
Mirror, Dimension(5,68): 6
Mirror, Dimension(6,57): 4
Mirror, Dimension(7,49): 10
Mirror, Dimension(8,43): 11
Mirror, Dimension(9,38): 10
Mirror, Dimension(10,34): 15
Mirror, Dimension(11,31): 20
Mirror, Dimension(12,29): 13
Mirror, Dimension(13,27): 18
Mirror, Dimension(14,25): 27
Mirror, Dimension(15,23): 21
Mirror, Dimension(16,22): 23
Mirror, Dimension(17,20): 18
Mirror, Dimension(18,19): 25
Mirror, Dimension(19,18): 29
Mirror, Dimension(20,17): 31

And sliding unigram repeats (funny coincidence, first 5 are square numbers):

Normal, Dimension(2,170): 4
Normal, Dimension(3,114): 9
Normal, Dimension(4,85): 16
Normal, Dimension(5,68): 25
Normal, Dimension(6,57): 36
Normal, Dimension(7,49): 48
Normal, Dimension(8,43): 63
Normal, Dimension(9,38): 82
Normal, Dimension(10,34): 104
Normal, Dimension(11,31): 130
Normal, Dimension(12,29): 158
Normal, Dimension(13,27): 189
Normal, Dimension(14,25): 226
Normal, Dimension(15,23): 269
Normal, Dimension(16,22): 314
Normal, Dimension(17,20): 364
Normal, Dimension(18,19): 419
Normal, Dimension(19,18): 477
Normal, Dimension(20,17): 538

Mirror, Dimension(2,170): 4
Mirror, Dimension(3,114): 9
Mirror, Dimension(4,85): 17
Mirror, Dimension(5,68): 27
Mirror, Dimension(6,57): 41
Mirror, Dimension(7,49): 59
Mirror, Dimension(8,43): 80
Mirror, Dimension(9,38): 104
Mirror, Dimension(10,34): 134
Mirror, Dimension(11,31): 165
Mirror, Dimension(12,29): 200
Mirror, Dimension(13,27): 238
Mirror, Dimension(14,25): 282
Mirror, Dimension(15,23): 328
Mirror, Dimension(16,22): 379
Mirror, Dimension(17,20): 435
Mirror, Dimension(18,19): 496
Mirror, Dimension(19,18): 561
Mirror, Dimension(20,17): 630

Here are unigram repeats + cipher offset. Per 17 means 17 by 20 basically.

Grouped unigram repeats, offsets: 
---------------------------------------------------------
Per 2: 2, 2
Per 3: 3, 2, 4
Per 4: 4, 5, 5, 2
Per 5: 3, 5, 5, 7, 5
Per 6: 6, 5, 6, 4, 6, 9
Per 7: 6, 6, 9, 8, 6, 8, 5
Per 8: 7, 8, 8, 6, 9, 9, 8, 8
Per 9: 9, 10, 8, 7, 11, 12, 8, 8, 9
Per 10: 7, 9, 9, 10, 10, 10, 12, 13, 14, 10
Per 11: 14, 11, 10, 12, 12, 11, 12, 13, 12, 11, 12
Per 12: 11, 14, 14, 12, 14, 13, 12, 14, 14, 14, 14, 12
Per 13: 14, 14, 15, 16, 15, 18, 19, 15, 15, 13, 12, 11, 12
Per 14: 17, 16, 15, 15, 13, 13, 12, 15, 16, 17, 20, 18, 18, 21
Per 15: 16, 17, 16, 15, 16, 14, 16, 19, 21, 20, 19, 19, 20, 22, 21
Per 16: 17, 19, 20, 16, 20, 20, 19, 18, 19, 21, 19, 20, 22, 24, 21, 23
Per 17: 18, 17, 20, 24, 27, 27, 22, 19, 19, 22, 25, 21, 22, 21, 24, 23, 20 <----------------
Per 18: 24, 25, 22, 24, 25, 25, 23, 23, 21, 24, 23, 18, 20, 23, 26, 26, 27, 28
Per 19: 24, 23, 21, 20, 20, 20, 25, 26, 27, 29, 30, 29, 29, 28, 28, 27, 26, 28, 28
Per 20: 25, 26, 25, 27, 32, 34, 31, 32, 32, 30, 25, 24, 24, 26, 27, 26, 25, 28, 29, 27

And the same thing but then for the amount of rows which have no repeats + offsets:

Row count without unigram repeats, offsets:
---------------------------------------------------------
Row length 2: 168, 168
Row length 3: 110, 109, 111
Row length 4: 81, 83, 80, 80
Row length 5: 65, 63, 62, 63, 63
Row length 6: 50, 47, 50, 52, 51, 52
Row length 7: 43, 43, 41, 42, 40, 40, 43
Row length 8: 36, 35, 34, 33, 34, 37, 35, 35
Row length 9: 30, 29, 29, 29, 27, 28, 31, 30, 29
Row length 10: 27, 25, 24, 24, 24, 25, 26, 26, 27, 27
Row length 11: 20, 21, 21, 21, 18, 20, 23, 24, 24, 24, 23
Row length 12: 21, 19, 16, 17, 17, 19, 19, 17, 17, 18, 18, 18
Row length 13: 18, 18, 17, 15, 14, 14, 14, 12, 13, 14, 16, 17, 17
Row length 14: 12, 9, 12, 12, 11, 12, 14, 14, 15, 16, 16, 13, 11, 11
Row length 15: 11, 7, 6, 8, 8, 11, 11, 10, 11, 12, 12, 11, 12, 11, 10
Row length 16: 8, 7, 10, 7, 7, 7, 6, 7, 10, 10, 9, 8, 10, 11, 9, 8
Row length 17: 9, 7, 5, 4, 9, 8, 9, 8, 8, 9, 7, 6, 4, 3, 3, 6, 7 <----------------
Row length 18: 3, 1, 0, 1, 2, 4, 7, 7, 6, 8, 7, 7, 7, 4, 4, 2, 5, 2
Row length 19: 3, 2, 2, 2, 1, 3, 1, 1, 1, 2, 2, 4, 4, 4, 8, 6, 4, 4, 3
Row length 20: 3, 3, 2, 2, 1, 3, 3, 2, 3, 4, 4, 2, 1, 2, 1, 0, 1, 2, 4, 3

Available in AZdecrypt under Statistics, Unigrams. If you put the cipher in 20 by 17 then the program will check up to 20, so increase the first dimension to increase the reach of the analysis. Dimensions can be changed under Functions, Dimensions.

Another good exercise would be to just encode a homphonic message by hand to see what it is like to try to not repeat. I like the idea of something simple, like 15 columns and just not repeating by row it seems a lot easier of a rule to follow than the sliding window rule.

i’ve done that several times with the benefit of knowing what you guys are looking for (and the benefit of azdecrypt letting me know how i’m doing). the natural tendency is to keep a separate list of symbols and mark each time they are used. this balances overuse of individual symbols but does not prevent repeating symbol pairs. it’s easy to visually inspect each row for repeats, but i had to go back and manually make sure i wasn’t using "XY" "XY" "XY" symbol pairs too often through the cipher. to do that i kept a separate page of common letter pairs (e.g. the letter "E" with basically any other letter), but even then it becomes exhausting to do manually. my belief is zodiac would have done this manually for a while then given up. he’s never shown stamina in any of his efforts (low effort killings, low effort writings, low effort 408). one way i cheated in avoiding these pairs was to make a symbol pair equal a letter (e.g. "+^" = "E", "+0"="A", etc). the high usage of "+" could indicate some additional step or place marker.

We were able to make the distinctive 26 L=17 shape with a palindromic cycle A B C D C B A B C D C B A.

Yes, but did you also see the high number of true-lengths in L17-L19 like z340?

I can imagine that the basic distribution shape for non-repeat strings like z340 would be found through different approaches, but wondered whether that always occurred with the true-lengths spike for L17-L19 also seen? For me, your stacked bar chart says quite a lot more than the original plain bar chart of non-repeat lengths.

The palindromic message is here:

http://zodiackillersite.com/viewtopic.p … 6&start=90

It looks just like the 340 after you take out the + symbols. I did not put a high count symbol in the palindromic message like the + and this is what it looks like with the genuine lengths marked red.

http://zodiackillersite.com/viewtopic.p … 6&start=90

Not the same. It is like comparing apples to oranges though as far as the + is concerned and the 340 is also not palindromic.

Here are the genuine lengths of the 340 sorted, with the repeated symbols at the beginning and end.

05 06 07 08 09 10 11 12 13 14 15 16 17 18 05 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 20
20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19 11 36 28 45 40 20 31 21 23 05 07 28
37 31 23 16 29 36 06 03 41 11 30 50 14 53 37 28 19 52 20 51 40 63 47 42 34 22 19
20 34 55 38 19 03 54 50 48 02 11 25 27 20 05 61 14 37 31 23 16 29 36 06 03
28 45 40 20 31 21 23 05 07 28 32 37 57 15 16 03 36 14 19 13 12 63 56 29 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 20 34 35 36 37 19 38 39 15 26
19 34 20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19 11 36 28 45 40 20
26 36 09 23 42 01 14 54 21 33 05 11 51 10 17 26 29 43 48 20 46 27 23
03 54 50 48 02 11 25 27 20 05 61 14 37 31 23 16 29 36 06 03 41 11
33 20 34 35 36 37 19 38 39 15 26 21 33 13 22 40 01 41 42 05 05
51 06 23 55 30 17 56 10 51 04 16 25 21 22 50 19 31 57 24 58 16
16 25 21 22 50 19 31 57 24 58 16 38 36 59 15 08 28 40 13 11 21
19 39 03 16 51 20 36 34 62 63 53 31 55 40 06 38 08 19 07 41 19
51 40 63 47 42 34 22 19 18 11 50 51 20 36 21 58 44 03 06 15 51
26 27 28 29 30 31 32 33 20 34 35 36 37 19 38 39 15 26 21 33
19 61 19 39 03 16 51 20 36 34 62 63 53 31 55 40 06 38 08 19
19 23 05 43 29 51 20 34 55 38 19 03 54 50 48 02 11 25 27 20
11 25 27 20 05 61 14 37 31 23 16 29 36 06 03 41 11 30 50 14
20 46 27 23 20 30 55 56 36 04 37 25 01 18 05 10 42 40 39 23
19 40 48 49 17 11 50 51 09 19 52 53 10 54 05 44 03 07 51
51 09 19 52 53 10 54 05 44 03 07 51 06 23 55 30 17 56 10
15 08 28 40 13 11 21 15 16 41 32 49 22 23 19 46 18 27 40
51 20 36 21 58 44 03 06 15 51 18 07 32 50 16 53 61 28 36
36 21 58 44 03 06 15 51 18 07 32 50 16 53 61 28 36 08 53
19 19 34 20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19
26 56 40 26 36 09 23 42 01 14 54 21 33 05 11 51 10 17 26
19 03 31 16 46 47 37 19 40 48 49 17 11 50 51 09 19
14 37 31 23 16 29 36 06 03 41 11 30 50 14 53 37
19 52 20 51 40 63 47 42 34 22 19 18 11 50 51
19 07 41 19 23 05 43 29 51 20 34 55 38 19
19 13 12 63 56 29 19 51 06 26 20 11 33 13
19 46 18 27 40 19 60 13 47 17 29 37 19
05 43 07 06 44 30 08 45 05 23 19 19
05 05 43 07 06 44 30 08 45 05
19 60 13 47 17 29 37 19 61 19
19 19 03 31 16 46 47 37 19
53 61 28 36 08 53 48 19 19
19 19 33 26 56 40 26

It sort of curves up from the bottom, flattens out at L=17-19, and then curves again toward the top. What is different about the flat ones that contribute so much to 26 L=17?

EDIT:

I separated the genuine lengths into groups, short varying, flat L17-19, and long varying. The repeated boundary symbols are included, and their frequencies are in the left and right columns. I highlighted a couple of short interesting and probably just coincidental patterns of symbol shape. If you count the rows in flat and long varying, they add up to 26, thus 26 L=17.

I separated the genuine lengths into groups, short varying, flat L17-19, and long varying. The repeated boundary symbols are included, and their frequencies are in the left and right columns. I highlighted a couple of short interesting and probably just coincidental patterns of symbol shape. If you count the rows in flat and long varying, they add up to 26, thus 26 L=17.

It might be meaningless, but you can read "BOO" from those characters as on Zodiac’s Halloween card.

I separated the genuine lengths into groups, short varying, flat L17-19, and long varying. The repeated boundary symbols are included, and their frequencies are in the left and right columns. I highlighted a couple of short interesting and probably just coincidental patterns of symbol shape. If you count the rows in flat and long varying, they add up to 26, thus 26 L=17.

It might be meaningless, but you can read "BOO" from those characters as on Zodiac’s Halloween card.

I don’t see any words at all.

I separated the genuine lengths into groups, short varying, flat L17-19, and long varying.

Nice. Great visualisation again, and a good choice of where to chop the strings to help highlight any patterns.

I notice that the L17s tend to have a short lead in, followed by a long gap between the repeating characters (obviously adding up to 17 in length). Similar for L18s. But L19s it’s the other way around, the repeated symbols tend to be closer together.

Are you able to easily colour the symbols above to show the 2 sections contributing to the length overall?

So for example, on the first L17 (row 23 on your grid above), highlight the + to the filled in circle in one shade, and the F to F repeat in another shade.

For the L17’s, the length between repeats appears to gradually increase by 2 (although not consistently). In fact, there’s a lot of "nearly" patterns, including the L17-L19 lengths themselves. Clearly I’m at the bottom of quite a deep hole here, so maybe not worth digging much further, but I wondered if this is similar to "complification", where there would be a string pattern of repeats around L17, if it were not broken up by (e.g.) filling in circles.

Here is similar to what you ask. Pinkish color is repeat from left end, greenish color is repeat from right, except that if they are the same pinkish only.

Some lengths overlap each other so if you look for a sequence in particular, you might find it in another length. They are sorted first by appearance order, then by size.

I wonder what the genuine lengths might tell us about the shape of the key. Is it possible to have 26 L>=17 with any 1:1 assignments, and if so, how many?

The "add another homophone to the group to avoid repeats within a sliding window" hypothesis is more understandable to me at least looking at it this way.

There is a link to Largo’s awesome font on this page:

http://zodiackillersite.com/viewtopic.p … &start=760

And a vlookup table for converting numbers to symbols:

01 H
02 E
03 R
04 >
05 p
06 l
07 ^
08 V
09 P
10 k
11 |
12 1
13 L
14 T
15 G
16 2
17 d
18 N
19 +
20 B
21 (
22 #
23 O
24 %
25 D
26 W
27 Y
28 .
29 <
30 *
31 K
32 f
33 )
34 y
35 :
36 c
37 M
38 U
39 Z
40 z
41 J
42 S
43 7
44 8
45 3
46 _
47 9
48 t
49 j
50 5
51 F
52 &
53 4
54 /
55 –
56 C
57 q
58 ;
59 X
60 @
61 b
62 A
63 6

H E R > p l ^ V P k | 1 L T G 2 d
N p + B ( # O % D W Y . < * K f )
B y : c M + U Z G W ( ) L # z H J
S p p 7 ^ l 8 * V 3 p O + + R K 2
_ 9 M + z t j d | 5 F P + & 4 k /
p 8 R ^ F l O – * d C k F > 2 D (
# 5 + K q % ; 2 U c X G V . z L |
( G 2 J f j # O + _ N Y z + @ L 9
d < M + b + Z R 2 F B c y A 6 4 K
– z l U V + ^ J + O p 7 < F B y –
U + R / 5 t E | D Y B p b T M K O
2 < c l R J | * 5 T 4 M . + & B F
z 6 9 S y # + N | 5 F B c ( ; 8 R
l G F N ^ f 5 2 4 b . c V 4 t + +
y B X 1 * : 4 9 C E > V U Z 5 – +
| c . 3 z B K ( O p ^ . f M q G 2
R c T + L 1 6 C < + F l W B | ) L
+ + ) W C z W c P O S H T / ( ) p
| F k d W < 7 t B _ Y O B * – C c
> M D H N p k S z Z O 8 A | K ; +

The "add another homophone to the group to avoid repeats within a sliding window" hypothesis is more understandable to me at least looking at it this way.

I guess there are many ways to go about the "no repeat window" hypothesis and adding homophones to a 1:1 key when needed is one of them. But you could also have a pre existing key and work with that, which may be a more probable assumption since that still allows for high frequency symbols. Another interesting possibility is that Zodiac used a "no repeat window" more sparingly or unconsciously, for example to avoid obvious bigram repeats.

Here is similar to what you ask.

Thanks.

Turns out it isn’t as interesting visually as it is numerically.

So we’ve broadly got structures like this…

A….BC….B….D……ED……
…….^—————–^
Where the distance C to E has a higher prominence for 17,18 or 19.

Or
A….BC….D….B……ED……
…….^—————–^

And some other variations where there are symbol pairs and gaps of zero, but fundamentally the same pattern.