Hi,
A couple of days ago I read the encyclopedia of observations (again) and stumbled upon Scott Akin’s observation:
http://zodiackillerciphers.com/wiki/index.php?title=Encyclopedia_of_observations#Other_observations_2 (Second last entry)
From Scott Akin: All occurrences of the "H" symbol are involved with this observation: Consider the rectangular regions formed by the corners highlighted in this illustration Illustration:
http://zodiackillerciphers.com/images/80-character-rectangles.png. Each region is exactly 80 characters in size (4×20 and 5×16), and there is symmetry to the corner symbols.
I found his observation very interesting and searched this forum but I did not found a corresponding thread. So I started some analysis to find out how often such patterns (I will call them „Box Markers“) occur by chance. The result is unfortunately not what I expected since I hoped such box markers are very rare. It seems that Scott’s promising observation is just another red herring 
Here is what I did:
I have implemented a function into my python library which can extract all box markers which are found in a given text. I ran a test with z340 and found 11 rectangles which are surrounded by box markers. After that I ran the same test with z408 and got 21 finds. Then I ran 10000 tests with random shuffled versions of z340 (with original symbol frequencies) and got the following results:
Lowest count of found rectangles: 0
Highest count of found rectangles: 22
Average count of found rectangles: 9
Rectangle count : Ciphers with this count
0 : 2
1 : 4
2 : 35
3 : 109
4 : 207
5 : 414
6 : 717
7 : 972
8 : 1199
9 : 1368
10 : 1253
11 : 1128
12 : 867
13 : 645
14 : 464
15 : 288
16 : 152
17 : 91
18 : 46
19 : 22
20 : 10
21 : 6
22 : 1
Because of the high amount of found box markers I did not made any further tests (ignore overlapping rectangles, check symmetries and so forth). I am quite sure that Scott Akin’s observations is just a coincidence (Sorry Scott )
Here are my worksheets. I have marked the rectangles in multiple tables for a better overview:
Box markers in z340:
Box markers in z408:
Thank you very much for doing this test! It is something I had been wanting to do for a while now.
The other remaining question about that observation would be: How often do a pair of rectangles share the same covered area? (For example, Scott’s box markers each cover 80 characters). My guess is that such a pair will often be found, due to the high frequency of random occurrences of box markers in general.
Largo,
Thank you for looking at the box corners!
I find two facts about the box corners interesting:
1. The vertical symmetry. Both box corners are centered between the top and the bottom; and
2. The count of symbols involved. There are only 4 of the H symbols, as I count by eye, and all 4 of them are involved. There are only 4 of the > and 5 of the theta as I count by eye.
If you had 1:1 substitution with one symbol for each letter, then you would have a lot of box symbols. But as you increase the count of symbols for homophonic, then the higher count symbols would more likely be involved with a box corner. I would expect the + to be involved. But here, we have only 4 of the H, and all four are box corners and symmetrically positioned.
Consider calculating the probability of this occurrence, based on the count of symbols involved, and compare. Are there other box corners with symbols that have such a low count?
What about symmetry? Are there any other pairs of box corners that are vertically or horizontally centered?
Nice work Largo. I like your .pdf presentations.
