View source for Comparison of sequence repetition rates

This is a comparison of repeated sequences in both the 408 and 340 ciphers.

Note: I am using the [[Webtoy's transcription scheme]].

These sequences are derived from reading the cipher as normal text (from left to right, top to bottom).

==Digrams==

{|style="border-collapse: separate; border-spacing: 0; border-width: 1px; border-style: solid; border-color: #000; padding: 0"
|-valign="top"
! style="border-style: solid; border-width: 1px"|  Repeated digrams in the 408
! style="border-style: solid; border-width: 1px"|  Total repeated digrams 
! style="border-style: solid; border-width: 1px"|  Repeated digrams in the 340
! style="border-style: solid; border-width: 1px"|  Total repeated digrams
|-valign="top"
| style="border-style: solid; border-width: 1px"| #B (6), q_ (4), qE (3), VW (3), OR (3), LM (3), BP (3), A9 (3), 9% (3), 9# (3), r\ (2), r9 (2), qW (2), qG (2), eG (2), cZ (2), c+ (2), _T (2), ^R (2), Xq (2), Wq (2), WV (2), WI (2), VE (2), UI (2), Tt (2), TY (2), S) (2), RU (2), PO (2), P# (2), L( (2), Ik (2), I( (2), HM (2), GY (2), EH (2), DR (2), BV (2), B% (2), AP (2), @X (2), 7L (2), 75 (2), 6q (2), /9 (2), +q (2), (S (2), %% (2)
| style="border-style: solid; border-width: 1px"| 112 (49 unique digrams)
| style="border-style: solid; border-width: 1px"|  M+ (3), G2 (3), FB (3), ++ (3), p7 (2), UZ (2), Op (2), O+ (2), Np (2), I5 (2), Fl (2), By (2), Bc (2), 8R (2), 5F (2), +R (2), +& (2), )L (2), () (2), (# (2), #O (2)
| style="border-style: solid; border-width: 1px"|  46 (21 unique digrams)
|}

==Trigrams==

{|style="border-collapse: separate; border-spacing: 0; border-width: 1px; border-style: solid; border-color: #000; padding: 0"
|-valign="top"
! style="border-style: solid; border-width: 1px"|  Repeated trigrams in the 408
! style="border-style: solid; border-width: 1px"|  Total repeated trigrams 
! style="border-style: solid; border-width: 1px"|  Repeated trigrams in the 340
! style="border-style: solid; border-width: 1px"|  Total repeated trigrams
|-valign="top"
| style="border-style: solid; border-width: 1px"|  9#B (3), qEH (2), eGY (2), _TY (2), UIk (2), POR (2), P#B (2), EHM (2), #BV (2), #BP (2)
| style="border-style: solid; border-width: 1px"|  21 (10 unique trigrams)
| style="border-style: solid; border-width: 1px"|   I5F (2), FBc (2)

| style="border-style: solid; border-width: 1px"|  7 (2 unique trigrams)
|}

==4-grams==

{|style="border-collapse: separate; border-spacing: 0; border-width: 1px; border-style: solid; border-color: #000; padding: 0"
|-valign="top"
! style="border-style: solid; border-width: 1px"|  Repeated 4-grams in the 408
! style="border-style: solid; border-width: 1px"|  Total repeated 4-grams 
! style="border-style: solid; border-width: 1px"|  Repeated 4-grams in the 340
! style="border-style: solid; border-width: 1px"|  Total repeated 4-grams
|-valign="top"
| style="border-style: solid; border-width: 1px"|   qEHM (2), 9#BP (2)
| style="border-style: solid; border-width: 1px"|  4 (2 unique 4-grams)
| style="border-style: solid; border-width: 1px"|  None

| style="border-style: solid; border-width: 1px"|  0 (0 unique 4-grams)
|}

No repeats exist in either cipher for n-grams where n is greater than 4.

==N-grams, in multiple rotations and mirrored arrangements==

This n-gram analysis was performed upon various rotations.  First, the cipher is rotated 0 and 90 degrees clockwise.  Each resulting ciphertext's repeated n-grams are tallied.  For the second part of the analysis, the cipher is first flipped horizontally, and then rotated 0 and 90 degrees clockwise.  The resulting ciphertext's repeated n-grams are again tallied.  

Rotations to 180 and 270 degrees are excluded for brevity, because the repeated n-gram counts are identical to the 0 and 90 degree cases, respectively.

Maximum non-zero repeated n-gram counts are in boldface for each combination of cipher and value of N.

{| class="wikitable sortable" style="border-collapse: separate; border-spacing: 0; border-width: 1px; border-style: solid; border-color: #000; padding: 0"
|-valign="top"
! style="border-style: solid; border-width: 1px"|  N
! style="border-style: solid; border-width: 1px"|  Flip/Rotation
! style="border-style: solid; border-width: 1px"|  Total repeated n-grams in the 408
! style="border-style: solid; border-width: 1px"|  Total unique repeated n-grams in the 408
! style="border-style: solid; border-width: 1px"|  % of ciphertext covered by repeats
! style="border-style: solid; border-width: 1px"|  Total repeated n-grams in the 340
! style="border-style: solid; border-width: 1px"|  Total unique repeated n-grams in the 340
! style="border-style: solid; border-width: 1px"|  % of ciphertext covered by repeats
|-valign="top"
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   No/0
| style="border-style: solid; border-width: 1px"|   <b>112</b>
| style="border-style: solid; border-width: 1px"|   <b>49</b>
| style="border-style: solid; border-width: 1px"|   <b>27%</b>
| style="border-style: solid; border-width: 1px"|   46
| style="border-style: solid; border-width: 1px"|   21
| style="border-style: solid; border-width: 1px"|   14%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   No/90
| style="border-style: solid; border-width: 1px"|   34
| style="border-style: solid; border-width: 1px"|   17
| style="border-style: solid; border-width: 1px"|   8%
| style="border-style: solid; border-width: 1px"|   40
| style="border-style: solid; border-width: 1px"|   17
| style="border-style: solid; border-width: 1px"|   12%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   Yes/0
| style="border-style: solid; border-width: 1px"|   106
| style="border-style: solid; border-width: 1px"|   47
| style="border-style: solid; border-width: 1px"|   26%
| style="border-style: solid; border-width: 1px"|   <b>54</b>
| style="border-style: solid; border-width: 1px"|   <b>25</b>
| style="border-style: solid; border-width: 1px"|   <b>16%</b>
|-valign="top"
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   Yes/90
| style="border-style: solid; border-width: 1px"|   42
| style="border-style: solid; border-width: 1px"|   20
| style="border-style: solid; border-width: 1px"|   10%
| style="border-style: solid; border-width: 1px"|   41
| style="border-style: solid; border-width: 1px"|   18
| style="border-style: solid; border-width: 1px"|   12%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   3
| style="border-style: solid; border-width: 1px"|   No/0
| style="border-style: solid; border-width: 1px"|   <b>21</b>
| style="border-style: solid; border-width: 1px"|   <b>10</b>
| style="border-style: solid; border-width: 1px"|   <b>5%</b>
| style="border-style: solid; border-width: 1px"|   <b>4</b>
| style="border-style: solid; border-width: 1px"|   <b>2</b>
| style="border-style: solid; border-width: 1px"|   <b>1%</b>
|-valign="top"
| style="border-style: solid; border-width: 1px"|   3
| style="border-style: solid; border-width: 1px"|   No/90
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   3
| style="border-style: solid; border-width: 1px"|   Yes/0
| style="border-style: solid; border-width: 1px"|   20
| style="border-style: solid; border-width: 1px"|   10
| style="border-style: solid; border-width: 1px"|   5%
| style="border-style: solid; border-width: 1px"|   <b>4</b>
| style="border-style: solid; border-width: 1px"|   <b>2</b>
| style="border-style: solid; border-width: 1px"|   <b>1%</b>
|-valign="top"
| style="border-style: solid; border-width: 1px"|   3
| style="border-style: solid; border-width: 1px"|   Yes/90
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   1
| style="border-style: solid; border-width: 1px"|   1%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   4
| style="border-style: solid; border-width: 1px"|   No/0
| style="border-style: solid; border-width: 1px"|   <b>4</b>
| style="border-style: solid; border-width: 1px"|   <b>2</b>
| style="border-style: solid; border-width: 1px"|   <b>1%</b>
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   4
| style="border-style: solid; border-width: 1px"|   No/90
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   4
| style="border-style: solid; border-width: 1px"|   Yes/0
| style="border-style: solid; border-width: 1px"|   2
| style="border-style: solid; border-width: 1px"|   1
| style="border-style: solid; border-width: 1px"|   0%
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
|-valign="top"
| style="border-style: solid; border-width: 1px"|   4
| style="border-style: solid; border-width: 1px"|   Yes/90
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0
| style="border-style: solid; border-width: 1px"|   0%
|}

Observations:
* The maximum numbers of repeated digrams and trigrams occur for the original 408 cipher, when it is unaltered by flips and rotations.
* However, the maximum number of repeated digrams occurs for the 340 cipher when it is flipped horizontally.
** Also, the 340 cipher's repeated trigram count is unchanged by the horizontal flip.
Remaining questions:
* What is the significance of the increase in the maximum number of repeated digrams when the 340 cipher is flipped horizontally?
** Experiment: Using the known 408 key, generate random encipherments to fill the 408's cipher block with encipherments of random sentences.  Then, count the number of times that the encipherment of a random sentence results in ciphertext arrangements that produce maximum repeated digram counts when the ciphertext is rotated and/or flipped.