### 6 x 6 Torus in B3/S23

Posted:

**May 14th, 2018, 4:06 pm**This is my first attempt at the analysis of all possible patterns (2^36 = 68,719,476,736) on a 6x6 torus (under B3/S23 rules).

I have not done the CAP analysis that I have provided for the smaller tori. This may follow at a future timepoint with an improved software handling large (gigabyte-size) arrays.

The full listing (AshPix, AshPeriod and AshGen) has been stored in my Dropbox and can be accessed via the following link:

https://www.dropbox.com/s/mounf62998ad3 ... y.pdf?dl=0

Some observations:

-F

I have not done the CAP analysis that I have provided for the smaller tori. This may follow at a future timepoint with an improved software handling large (gigabyte-size) arrays.

Code: Select all

`ashPeriodCount`

p patternCount 2^36 pC [%]

1 58,627,717,276 68,719,476,736 85.31%

2 8,637,890,028 68,719,476,736 12.57%

3 1,296 68,719,476,736 0.00%

4 445,302,288 68,719,476,736 0.65%

6 37,948,536 68,719,476,736 0.06%

8 4,077,936 68,719,476,736 0.01%

12 202,887,504 68,719,476,736 0.30%

24 763,651,872 68,719,476,736 1.11%

The full listing (AshPix, AshPeriod and AshGen) has been stored in my Dropbox and can be accessed via the following link:

https://www.dropbox.com/s/mounf62998ad3 ... y.pdf?dl=0

Some observations:

- - 63.8% of all initial patterns end up with an empty torus

- An additional 21.5% end up with a non-empty still life

- An additional 12.6% end up in a p2 oscillator

- That leaves 2.1% which end up in an oscillator >= p3

- p3 is rare (only 1,296 patterns end up in a p3)

- The longest period is p24, quite common actually (wait for more information on this channel)

- 4.5 bn (!) - 6.6% - of all initial patterns end up in a 12-cell ash pattern, whereas only 1.1 million (~ 0.025% of the previous figure) end up in an 11-cell ash pattern

- No ash pattern (incl. the oscillators) contains more than 18 cells (this threshold happens to be exactly 50% of all cells) (50% maximum density - coincidence? or is this a proven law in B3/S23?)

- No pattern needed more than 90 generations to determine its fate

- The mean number of generations (to ash) has risen to 11.6 (from 8.1 for Tori of tSize=5)

-F