You might want to do this "properly" – I’ve done this by hand in a spread sheet, so may contain errors. This grid is an overlay for the 340, and the green squares show symbols that contribute to the second symbols of any repeated bigrams you get by doing skip-19.

Yellow is the first symbol of a bigram, and dark green is a symbol that is both the start of one bigram and the end of another. Green is what matters

This appears to be a negative result. I was looking to see if the greens biased to the right of the grid, indicating they might be caused by subconscious selection from a previous row. I can’t see a bias.

There are some vague patterns though. I’m not sure if these are an artefact of how the skip-19 works though.

I note:
-Row 10 of z340 doesn’t appear to contribute any second symbol characters to skip-19 bigrams.
-Row 0 also doesn’t – but maybe that’s just how skip-19 works. I haven’t looked in detail.
-There’s a group of empty spaces in the bottom right corner, and possibly top right also.
-Some repeated L shapes, in the style of pivots.
-And a diagonal area of blanks in the top left, that would presumably turn into a column of blanks in skip-19.

Since this didn’t support my theory, I’ll just leave it out there in case it triggers a connection with something else.

CK

This appears to be a negative result. I was looking to see if the greens biased to the right of the grid, indicating they might be caused by subconscious selection from a previous row. I can’t see a bias.

I see, that is really clever!

CK ~

Some of those white spaces in the upper left and lower right show up again as two white vertical columns 3 and 4 f you cast the message into 19 columns, which lines up the P 19 symbols and makes it easier to look at. Start at position 3 and 4 , which are white, and skip 19 two symbols next to each other at a time. You will get white all the way to the bottom.

The 26 L = 17 observation is very interesting to me but I don’t have a hypothesis for it and think that there is a lot of possible work at a more granular level never done before. If you read through the message and go row by row, left to right, symbol by symbol, and when you get to a symbol that is already in that row, and mark it, you will only have 18 marked symbols by the time that you get to the end of the message. The repeaters by rows, I can’t remember what Jarlve calls them.

Cyclic homophonic messages don’t have so many strings of unique symbols as long as 17. There are 23 strings at L = 16, and 22 at L = 15 also. That hump in the chart that is shifted to the right would in a cyclic message be shifted more to the left, like a more uniform bell curve. Like this.

We were able to duplicate the same shape with palindromic cycles A B C D C B A B C D etc, which spreads some of the symbols farther away from each other. However, the message does not have palindromic cycles like that. There might be a few, not not as an encoding scheme in general. We tested the cycles using isometric cycle patterns. With each of the 1,953 two symbol combinations, assign the first appearing symbol A and the second B. Then write the pattern A B A B A B or whatever it is for that combination. Count or score how many consecutive alternations there are to figure out how cyclic the message is. Shuffle the message a lot of times, and compare the shuffled messages with the original. The message is cyclic A B A B like that. Try different patterns A B A A B A, of which there are a lot of also; try all patterns, shuffle, score, and compare to un-shuffled. The 340 is mostly cyclic A B A B we found out.

Jarlve’s recent testing shows that symbol selection within homophone groups is at around 15% random in the top half, and 35% random in the bottom half. We have known for a few years now that it is about 25% to 30% random if you look at it as a whole. Symbol selection and 26 L = 17 is related somehow, and I wonder if the randomness is what causes 26 L = 17. Maybe it is not random maybe the same thing that causes the message to appear 25 % random is what causes 26 L = 17. ?

What symbols cause 26 L = 17 still has not been looked at in detail, at least not that I can remember. I have a spreadsheet that shows the strings are in the message and how long they are. Where they are could be looked at more. Breaking up the symbols into groups. You would think that high frequency symbols contribute to the short strings, and low frequency symbols to the long strings, but is there a pattern that doesn’t make any sense?

What about casting the message into different numbers of columns and looking at that repeaters by rows pattern I talked about above some more, what happens to it. Is there a width that shows something interesting? I could buy the idea of a scytale message, and when he encoded he didn’t want to use the same symbol with each pass around the cylinder, and if his cycles took him to a repeat, he would skip or choose random from his homophone groups. To me, something simple, mechanical, but not so much subconscious just 1969 pencil and paper simple.

See below column chart of 26 L = 17. X axis is message position, Y axis is length of string. If you cut horizontally at Y = 17, you will find 26 columns that tall. But I am just not so sure that is what is important on the chart. I will consider working on this subject some more in the future.

The 26 L = 17 observation is very interesting to me […]

I’m going to have to have a chew on all this. I know it’s a simple thing, but that first chart has to rank as one of the most interesting observations I’ve seen. What an incredibly distinctive shape. I would be amazed if this didn’t lead to an answer, even if not a solution.

At the very least it seems to be screaming that horizontal is special. Can it also tell us whether grid is special, vs it just being 340 sequential characters like 408?

Does p17 have any particularly interesting shape in this analysis?

CK

We have also looked at the cycle A B A B pattern and other cycle patterns going from two directions from each of four corners and it is most cyclic reading left right top bottom.

What is grid? I don’t know what you mean by how P17 relates to 26 L + 17? In the picture I just put up above, on the left are the 18 symbols that repeat in their rows. I use numbers for symbols. With the flatter bell curve, it is of a message that is not quite as cyclic as the 340, there are 33 repeats in rows.

Can it also tell us whether grid is special, vs it just being 340 sequential characters like 408?

What I mean is, does the shape of the "26 L=17" distribution confirm that the grid the 340 is written on (17×20) is relevant to the cipher process, as opposed to it being just 340 symbols in sequence without any 2-dimentional structure? Obviously the maximum peak at length 17 is the width of the cipher, but do we see any particular pattern aligned with the actual rows of the 17×20 grid?

For 408 we know the grid layout doesn’t play a part in the cipher (at least for the part that deciphers). You could obviously decipher 408 without knowing it was written in a grid.

I come back to the idea that if the Zodiac was just writing a random sequence of symbols, he might have been trying to avoid repetitions – perhaps on an original row of width 17. But then there was some rearrangement that means it wasn’t the same rows we ended up with.

Does p19 have any particularly interesting shape in this analysis?

What I mean there is, if you take the resulting output from p19 (skip-19) that generates the high bigram repetitions, what does the distribution of non-repeating lengths then look like for that? Does the pattern disappear and revert to a distribution closer to a shuffled cipher? That would imply p19 is (err) less interesting (statistically) that 340 on its own. As in, evidence that p19 is just coincidence.

I don’t know for myself if there is any relationship between the 17 x 20 grid and 26 L=17. There are a lot of unique strings longer than 17, and with each position move left right top bottom, they get shorter by one. Keep in mind that the unique string lengths measure the distance between A and B2, where the string is A…B1….B2. It does not measure the distance between B1 and B2, which can vary. However, it works really well to give us a different perspective on cycles.

I don’t know the answer to your question about removing P19 symbols. More work could definitely be done to figure out what causes 26 L=17. We just don’t really know. Read here, a few pages before this page, this page, and several pages after.

http://zodiackillersite.com/viewtopic.p … 6&start=70 ( EDIT: Read also the 6th post here at the bottom regarding P19 and read also the bottom post here too I guess my batch of test messages did result in a few that look like the 340 ).

See Doranchak’s conclusion in the second post here:

http://zodiackillersite.com/viewtopic.p … &start=110

Read this short thread:

http://zodiackillersite.com/viewtopic.php?f=81&t=3616

And my short continuation 5th post here:

http://zodiackillersite.com/viewtopic.p … &start=790

What is the relationship between the cycles and 26 L = 17?

I wonder how the start and stop positions for the unique strings of length about 17 compare with the period 19 bigram repeat symbol positions. My guess is that, since the + is highest count with 24, it is most frequently terminating unique strings. And because it is heavily represented in the period 19 repeats, I guess that those positions would match up. But I haven’t looked.

And I don’t think that I ever did.

http://zodiackillersite.com/viewtopic.p … 6&start=70

If you are interested, that is one idea to look into.

Here are the start and stop positions for the 26 L = 17.

Oh man, there’s a lot of back reading to consume.
Whilst I’m reading that (forgive me if this is already covered…)

Keep in mind that the unique string lengths measure the distance between A and B2, where the string is A…B1….B2. It does not measure the distance between B1 and B2, which can vary.

This means each length of 17 is made up from the section A…B1 (like a tail) and then the repeat distance B1..B2

Here are the start and stop positions for the 26 L = 17.

As well as plotting the start and end locations, is it easy to add in the squares where the tails end?

I note there where you have a length of 17, you are likely to have a length of 16 within it, and 15, 14 etc, up to the point where the critical repeating symbol begins. So there’s some granularity to the lengths of 17 not shown on your image.

Find a start position, green. At L=17, the symbol directly below it is the repeated symbol. Look to the right of the green symbol for a yellow symbol that is the repeated symbol. The symbol to the left of the symbol directly below the green symbol is the last symbol.

For example, at position 2 is the E. Just below it is backward P. Find the repeated backward P at position 5. The end of the sequence is the N at position 18.

Thank you.

I’m not sure anything screams out of course.

(If I’ve got this right…) here is a heat map of the unique string lengths from their positions:

I was pondering why there were more 17 lengths than 16 or 18. Any why the cliff edge after 17. From this you can visualise the numerics behind that:

– every 17 "contains" (is to the left of) a 16 (except 3 where a new string starts) -> 3 more 17’s than 16’s
– every 16 "is within" (is to the right of) a 17 with no exceptions. So no strings begin with a 16 length alone. 16 is thus not really a length of interest in it’s own right, just a sub-length of the 17s.
– every 18 "contains" a 17, except one where a new string starts -> so one more 18 than a 17…except that….
– there are 7 lots of 17-lengths that start a new string without an 18, so in total there are 6 more 17s than 18s

So that’s the DNA of why there are more 17s than 16s or 18s.

By hand I can see that the only genuine starting lengths are 5,7,8,11,12,13,17,18,19,21,22,23,25,26,29. All the other lengths are just a consequence of a larger length not ending.

Go figure. If that’s of any interest.

CK

I agree and I like your heatmap. In the future could you show column and row numbers so I can get reference to positions of other observations? Thanks and glad you are looking at the 340. We need people with fresh energy, ideas and minds here. Awesome work!

It is easy to chase down a rabbit hole with detailed analysis of any observation, but it is also good experience. We contemplate here before we chase most of the time. I think that maybe he did just try not to repeat symbols when encoding, looking back at the row he was encoding. Or there could be another explanation. I also think that some of these observations are related to each other and how they are related still has not been discovered.

It is good and healthy for me to have new people because it helps me re-visit all of these things. Thanks.

You are welcome.

Here’s some rows/column. I hope the convention is to start from one not zero.

I’ve also highlighted the genuine start of unique strings, so they stand out from the sub-lengths. [Edit – actually, I’ve missed loads – did it my hand, so I’ll fix that. Editx2, that should be it.]

I like how you separate into two categories genuine start and sub lengths. My convention starts at 1 yes.

A stacked column chart. Blue is sub lengths, and red is genuine start lengths. The spike at 17 is caused by a lot of genuine start lengths of 17, 18 and 19, plus a few over 20. I think that has been noted before a long time ago.. Otherwise the spike would be at 16.

That’s a great visualisation. One might even argue that 17,18 and 19 as a set are the key observations, rather than 17 alone. Perhaps 18 is the interesting point, with 17 and 19 just being overspill either side? I guess if you plot just the red values un-stacked, that will be quite a dramatic shape; perhaps more so than the peak of repeat bigrams in p19.

Perhaps, perhaps. Anyway, at least it’s a little clearer where the shape of that distribution originates from.

Are you able to generate the same stacked chart for the 408?

CK