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I couldn't find a thread for this on the old board or here. These have been discussed on Dave's site and on ZKF. I'm not starting this to discuss them but if there had been a thread I would have posted it there. So anything pivot related can be posted in here.

It's a pattern that will most likely be nothing more than just that but I thought it might be interesting. The connection to pivots is that it is clustered around the 2nd pivot in the 340.

I will use lower case characters to denote backwards characters.

If you are familiar with the 340 then you will be familiar with the FBc pattern. These 2 repeated sequences border and intersect the second pivot. There are other repeated sequences that 'surround' that pivot but I realised today that there is a definite one. Here it is. FBb



Now after the FB in each of those lines we have c and y.



One line above these we have those characters in sequence. FBcy



There's a lot of these clusters happening around that second pivot. The B's, the p's, the M's and that's leaving out the rest of the V's and C's and P's. Maybe interestingly the 'dots' that form an integral part of the pivot don't fall into this alternating pattern.



I don't have a clue what it means but I do find it curious that there seems to be a 'pattern' of clustering within the 340 and that this example centres around one of the pivots.

Trav, what pivots? (You should also show the pivots, no?)
Interesting btw, yep.

So those "first and second pivots" spotted by whats-his-name, are these, then, outlined in yellow. Right.

Thanks for posting these interesting observations, trav. I wonder if similar patterns can be discovered in the 408.

smithy wrote:So those "first and second pivots" spotted by whats-his-name, are these, then, outlined in yellow. Right.

Yup, that's the puppies.

traveller1st wrote:

smithy wrote:So those "first and second pivots" spotted by whats-his-name, are these, then, outlined in yellow. Right.

Yup, that's the puppies.

Just to add, I assume that this went without saying but then we aren't all spending our days staring at this thing. The 'cluster' also contains the previously mentioned FBc pattern. Highlighted here by T with a blue rectangle (sharp corners) viewtopic.php?f=81&t=856 . And below by moi. I've even included outlines for the pivotally challenged.

Another pattern intersects with the other pivot, too:

doranchak wrote:Another pattern intersects with the other pivot, too:

I like that one 'cause it lines up. Here it is in context with the pivots and my original repeated pattern.



Something that strikes me about those repeating patterns is that they both contain a diagonal offset. This is something that the pivots actually mostly consist of, I say mostly because obviously there is only one corner symbol in each but the rest of the pivot consist of matching diagonal offsets separated by 0,1,2 symbols working outward along each leg.

So I'm wondering about construction. As we all have for soooooo many years. The pivots though, what caused that, if anything? Something again we've wondered about but for slightly less years. And then there's the "crop marks" with the diagonally filled box symbols in each corner (another spot of Dave's). These are diagonal offsets as well.

I can't stop seeing diagonal "things" in this cipher. Maybe it's just staring fatigue from looking at as a grid all these years and trying to see something different. A grid of lines and columns. But it's not lines and columns, it's diagonals as well. Actually it could be viewed as just diagonals. Like so.



Now obviously this gives us two blocks of cipher text so lets 'squish' it all back together into the familiar grid.




Now. I've only given this a cursory glance but I think that's just got rid of the pivots. Following this line of thinking, assume this was the start point before the cipher was further fiddled with, does that suggest that applying this approach of, lets call it extreme transposition, actually creates pivots?

I guess one way to test that wold be to apply this to the 408. (Something to do later.)

Just to close for now. We started, on this section, with two diagonal grids and the image above shows them reconstituted in order, ie the first grid followed bye second. You could of course, when faced with two grids, further complicate matters by reversing their order before recombining them. So this is how that would look.



This does something interesting to the starting columns in each instance. it reverses their offset pattern depending on which combining order you go for. I have illustrated this below along with the original 340 for reference. I'm not saying any of this means anything but I thought it was worth exploring after thinking about offsets.



I have for quite a while now felt that the 340 is a substitution cipher albeit 'fiddled' with. It's not very scientific but throughout the hundreds of variations that I've ran through ZDK there seems to be something about the original, even though it doesn't yield a solution, if it's altered in certain ways it feels wrong. It seems to struggle to create anything coherent, sometimes even a single word. It's like it wants to be a substitution cipher but it can't quite make it. Half phrases seem to appear and words appears that seem to run into other words and at times it's almost like there's some kind of wrap around thing happening where, regardless of the plaintext, it joins things and splits things in similar places. Like a jigsaw with square pieces

Probably all nothing as usual but I thought it was interesting in that it might address certain issues (pivots) or at least lead to someone realising something useful.

Here's the 408 with the above actions applied (split into 2 diagonal grids then rejoined). If anyone spots any pivots pls post. I can't get my eyes to focus at the moment. One thing I will say is that whilst recompiling these it hits home how much time Zodiac actually took on the 340 to get the thing to read comfortably with regards positioning of each symbol in relation to the symbols around it. He took the time to make sure that each one was centred comfortably so that the columns and lines appear as straight as they could be. This becomes clear when you look at the ones I've just done and whilst I've tried to balance the symbols some are probably out of line.