OK – so you are highlighting clusters where bigrams tend to start and end. Is that right?
I highlighted a repeating structure. It is possible that not all of these bigram repeats connect properly, in the 340 the repeating structure overlaps with itself and its boundaries are unclear. And there are indications of a third and fourth repeat (periodical). I think it will prove to be highly subjective to the grid dimensions.
I guess I’m getting confused about the distinction between clusters and structures.
What you are calling structures, I am seeing as a tendency for repeating bigrams to start near certain columns and to end near certain columns. The latter is a consequence of the former due to the fixed period. Are you seeing something to the structures that isn’t just this clustering phenomenon?
There’s something periodical about it.
In the 340, certain parts of the structure repeat 4 times. Let’s say that there are 4 structures, from left to right 1, 2, 3 and 4 and some of them are partial. Then some of the bigrams in structure 1 connect to structure 2, allot of bigrams in structure 2 connect to structure 3, some of the bigrams in structure 3 connect to structure 4. The shape of the structure and the offset it repeats in seems dominant here, and not for instance a clustering effect that creates a copy.
I like your idea but how would Zodiac have transposed it then? That seems a bit strange.
I am not really sure. It looks like the message above is 20 x 17. You redrafted the message into 19 columns, then rotated it so that the repeat symbols would be read horizontally, and then redrafted it again into 20 columns?
I am sorry if my description of what I did was a bit confusing. Here is a more detailed version:
Period 19 is the same like resizing the cipher to width 19 and reading it top to bottom, left to right. As we know, we get 37 bigram repeats by doing so.
Now imagine a slightly different transposition which has almost the same effect like period 19. To keep things easy I have created a „cipher“ made of „ABCD…“:
As you can see in the image each row is shifted to the left by formula „rowIndex * -2“ until -16 is reached. If you read this cipher (of course with the z340 symbols) top to bottom, left to right you will get 39 bigram repeats. The bigrams are of course almost the same like the bigrams from the period 19 version (see table from my last post in this thread). The sample cipher from my last post in this thread was created like that (z340 read top to bottom, left to right after applying the row shifts). Thus it is 20×17 (not redrafted).
As you can see in the image the shifting process has two breaks which can be seen as period 18 repeats. Maybe such breaks causes the misalignment you mentioned earlier smokie.
Long story made short: The high peak of repeated bigrams in period 19 may be the effect of a row shift like the one shown above. If you mention the 3 purple lines in the table you can imagine the row shifts as some sort of rail fence transposition too. Since period 19 / flipped + period 15 causes significant bigram peaks but do not lead to a solution we may have to look for slightly different modifications that are close to period 19.
Nothing much in that…but I do like that whole simplistic method of z making the 340 difficult using such a method.
I totally agree with you! Sometimes I think we don’t see the forest for the trees (is this translation correct?). Some sort of a home grown transpositioning method could lead to a cipher that remains unsolved for so many years.
OK I tried to reproduce the highlighted mirrored period 29 bigrams:
In my version, orange is only used to mark the 1st symbol of each bigram, and red is only used to mark the 2nd symbol of each bigram.
I think a lot of the "repeating structure" occurs only because they are already linked by period 29, which shows up in the grid as your x=5 y=2 rule. For example:
The structures formed by 
and 
are the same because they belong to the same set of bigrams linked by period 29.
Maybe there is some additional regularity you have noticed that I still don’t understand yet, but it just looks like the natural outcome of showing period 29 mirrored bigrams in a 17×20 non-mirrored grid. Which is still one possible explanation for the pivots: clusters of mirrored repeating period 29 bigrams.
Are you looking specifically at exceptions to the normal period 29 behavior? In other words, parts of the repeating patterns that aren’t explained by the above?
Ok Largo. Then the difference is that you would still need to undo the row shifts after untransposing period 19? Changing the order or offset of rows that are sufficiently long will not cause the cipher to become unsolvable. Maybe I misunderstood something.
Maybe there is some additional regularity you have noticed that I still don’t understand yet, but it just looks like the natural outcome of showing period 29 mirrored bigrams in a 17×20 non-mirrored grid. Which is still one possible explanation for the pivots: clusters of mirrored repeating period 29 bigrams.
I realize now what is causing the structure to exhibit hints of multiple repeats. If you look at period 1 bigrams then they may group together and form longer blocks. Translate that to period 29 and add some bigram regionality et voila. I suppose that’s what you meant with clustering.
Here’s my bigram map for period 29 in 29 columns, there is indeed quite allot of clustering here.
I like your idea but how would Zodiac have transposed it then? That seems a bit strange.
I am not really sure. It looks like the message above is 20 x 17. You redrafted the message into 19 columns, then rotated it so that the repeat symbols would be read horizontally, and then redrafted it again into 20 columns?
I am sorry if my description of what I did was a bit confusing. Here is a more detailed version:
Period 19 is the same like resizing the cipher to width 19 and reading it top to bottom, left to right. As we know, we get 37 bigram repeats by doing so.
Now imagine a slightly different transposition which has almost the same effect like period 19. To keep things easy I have created a „cipher“ made of „ABCD…“:As you can see in the image each row is shifted to the left by formula „rowIndex * -2“ until -16 is reached. If you read this cipher (of course with the z340 symbols) top to bottom, left to right you will get 39 bigram repeats. The bigrams are of course almost the same like the bigrams from the period 19 version (see table from my last post in this thread). The sample cipher from my last post in this thread was created like that (z340 read top to bottom, left to right after applying the row shifts). Thus it is 20×17 (not redrafted).
As you can see in the image the shifting process has two breaks which can be seen as period 18 repeats. Maybe such breaks causes the misalignment you mentioned earlier smokie.
Long story made short: The high peak of repeated bigrams in period 19 may be the effect of a row shift like the one shown above. If you mention the 3 purple lines in the table you can imagine the row shifts as some sort of rail fence transposition too. Since period 19 / flipped + period 15 causes significant bigram peaks but do not lead to a solution we may have to look for slightly different modifications that are close to period 19.Nothing much in that…but I do like that whole simplistic method of z making the 340 difficult using such a method.
I totally agree with you! Sometimes I think we don’t see the forest for the trees (is this translation correct?). Some sort of a home grown transpositioning method could lead to a cipher that remains unsolved for so many years.
Largo, check out the Department of the Army Technical Manual published 1955 Discussion of Route Transposition: https://www.nsa.gov/news-features/decla … 078809.pdf. There is a lot of discussion of simple route transposition in Chapter 2, and Chapter 8, which discusses different geometric shapes. Your idea reminds me of maybe a parallelogram or some similar shape.
Ok Largo. Then the difference is that you would still need to undo the row shifts after untransposing period 19? Changing the order or offset of rows that are sufficiently long will not cause the cipher to become unsolvable. Maybe I misunderstood something.
Row offset can cause the cipher to become unsolvable, my bad.
