X-Rule

[jmgomez]

A New Cellular Automata capable of logic Universality: X-Rule.

X-Rule is 2D, binary with a Moore Neighborhood like Game of Life, but
is no based on birth/survival and is non-isotropic.

for more details see:
http://arxiv.org/abs/1504.01434

[M. I. Wright]

Hm... I tried to make a Golly ruletable for the X-rule based on Figure 12 in the paper, but it didn't quite work out.

AtjWSL6.png (23.49 KiB) Viewed 626 times

I took 'descending order of neighborhood values' to mean counting down, in binary, from 111111111 to 000000000 - where the first digit represents the current cell and the remaining eight represent its Moore neighborhood - matching each row of the image to 64 numbers. (e.g. the first row, 0001001001100000000000010000010000101000011110100000010000010011, went to the neighbor counts 111111111 through 111000000.)

Code: Select all

@RULE not-x-rule
@TABLE

To open this rule, hit 'select all', copy it, then paste into Golly

n_states:2
neighborhood:Moore
symmetries:none

# The first digit represents the current cell, the next eight its Moore neighborhood, and the final digit determines that configuration's output
1,1,1,1,1,1,1,1,1,0
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,0,1,0
1,1,1,1,1,1,1,0,0,1
1,1,1,1,1,1,0,1,1,0
1,1,1,1,1,1,0,1,0,0
1,1,1,1,1,1,0,0,1,1
1,1,1,1,1,1,0,0,0,0
1,1,1,1,1,0,1,1,1,0
1,1,1,1,1,0,1,1,0,1
1,1,1,1,1,0,1,0,1,1
1,1,1,1,1,0,1,0,0,0
1,1,1,1,1,0,0,1,1,0
1,1,1,1,1,0,0,1,0,0
1,1,1,1,1,0,0,0,1,0
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,1,1,1,1,0
1,1,1,1,0,1,1,1,0,0
1,1,1,1,0,1,1,0,1,0
1,1,1,1,0,1,1,0,0,0
1,1,1,1,0,1,0,1,1,0
1,1,1,1,0,1,0,1,0,0
1,1,1,1,0,1,0,0,1,0
1,1,1,1,0,1,0,0,0,1
1,1,1,1,0,0,1,1,1,0
1,1,1,1,0,0,1,1,0,0
1,1,1,1,0,0,1,0,1,0
1,1,1,1,0,0,1,0,0,0
1,1,1,1,0,0,0,1,1,0
1,1,1,1,0,0,0,1,0,1
1,1,1,1,0,0,0,0,1,0
1,1,1,1,0,0,0,0,0,0
1,1,1,0,1,1,1,1,1,0
1,1,1,0,1,1,1,1,0,0
1,1,1,0,1,1,1,0,1,1
1,1,1,0,1,1,1,0,0,0
1,1,1,0,1,1,0,1,1,1
1,1,1,0,1,1,0,1,0,0
1,1,1,0,1,1,0,0,1,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,1,0,1,1,1,0
1,1,1,0,1,0,1,1,0,1
1,1,1,0,1,0,1,0,1,1
1,1,1,0,1,0,1,0,0,1
1,1,1,0,1,0,0,1,1,1
1,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,0,1,1
1,1,1,0,1,0,0,0,0,0
1,1,1,0,0,1,1,1,1,0
1,1,1,0,0,1,1,1,0,0
1,1,1,0,0,1,1,0,1,0
1,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,0,1,1,0
1,1,1,0,0,1,0,1,0,1
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,1,0,0,0,0
1,1,1,0,0,0,1,1,1,0
1,1,1,0,0,0,1,1,0,0
1,1,1,0,0,0,1,0,1,0
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,1,0
1,1,1,0,0,0,0,1,0,0
1,1,1,0,0,0,0,0,1,1
1,1,1,0,0,0,0,0,0,1
1,1,0,1,1,1,1,1,1,0
1,1,0,1,1,1,1,1,0,0
1,1,0,1,1,1,1,0,1,0
1,1,0,1,1,1,1,0,0,0
1,1,0,1,1,1,0,1,1,0
1,1,0,1,1,1,0,1,0,0
1,1,0,1,1,1,0,0,1,0
1,1,0,1,1,1,0,0,0,0
1,1,0,1,1,0,1,1,1,1
1,1,0,1,1,0,1,1,0,0
1,1,0,1,1,0,1,0,1,0
1,1,0,1,1,0,1,0,0,0
1,1,0,1,1,0,0,1,1,0
1,1,0,1,1,0,0,1,0,0
1,1,0,1,1,0,0,0,1,1
1,1,0,1,1,0,0,0,0,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,0,1,1,1,0,0
1,1,0,1,0,1,1,0,1,0
1,1,0,1,0,1,1,0,0,1
1,1,0,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,0,0
1,1,0,1,0,1,0,0,1,0
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,1,1,0
1,1,0,1,0,0,1,1,0,0
1,1,0,1,0,0,1,0,1,0
1,1,0,1,0,0,1,0,0,0
1,1,0,1,0,0,0,1,1,0
1,1,0,1,0,0,0,1,0,1
1,1,0,1,0,0,0,0,1,0
1,1,0,1,0,0,0,0,0,0
1,1,0,0,1,1,1,1,1,0
1,1,0,0,1,1,1,1,0,0
1,1,0,0,1,1,1,0,1,0
1,1,0,0,1,1,1,0,0,0
1,1,0,0,1,1,0,1,1,0
1,1,0,0,1,1,0,1,0,0
1,1,0,0,1,1,0,0,1,0
1,1,0,0,1,1,0,0,0,0
1,1,0,0,1,0,1,1,1,1
1,1,0,0,1,0,1,1,0,0
1,1,0,0,1,0,1,0,1,1
1,1,0,0,1,0,1,0,0,0
1,1,0,0,1,0,0,1,1,0
1,1,0,0,1,0,0,1,0,0
1,1,0,0,1,0,0,0,1,0
1,1,0,0,1,0,0,0,0,1
1,1,0,0,0,1,1,1,1,0
1,1,0,0,0,1,1,1,0,0
1,1,0,0,0,1,1,0,1,1
1,1,0,0,0,1,1,0,0,0
1,1,0,0,0,1,0,1,1,0
1,1,0,0,0,1,0,1,0,1
1,1,0,0,0,1,0,0,1,0
1,1,0,0,0,1,0,0,0,0
1,1,0,0,0,0,1,1,1,0
1,1,0,0,0,0,1,1,0,0
1,1,0,0,0,0,1,0,1,0
1,1,0,0,0,0,1,0,0,0
1,1,0,0,0,0,0,1,1,0
1,1,0,0,0,0,0,1,0,0
1,1,0,0,0,0,0,0,1,0
1,1,0,0,0,0,0,0,0,0
1,0,1,1,1,1,1,1,1,0
1,0,1,1,1,1,1,1,0,0
1,0,1,1,1,1,1,0,1,0
1,0,1,1,1,1,1,0,0,1
1,0,1,1,1,1,0,1,1,0
1,0,1,1,1,1,0,1,0,0
1,0,1,1,1,1,0,0,1,1
1,0,1,1,1,1,0,0,0,1
1,0,1,1,1,0,1,1,1,1
1,0,1,1,1,0,1,1,0,0
1,0,1,1,1,0,1,0,1,1
1,0,1,1,1,0,1,0,0,1
1,0,1,1,1,0,0,1,1,0
1,0,1,1,1,0,0,1,0,0
1,0,1,1,1,0,0,0,1,1
1,0,1,1,1,0,0,0,0,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,0,1,1,1,0,0
1,0,1,1,0,1,1,0,1,0
1,0,1,1,0,1,1,0,0,0
1,0,1,1,0,1,0,1,1,0
1,0,1,1,0,1,0,1,0,0
1,0,1,1,0,1,0,0,1,0
1,0,1,1,0,1,0,0,0,0
1,0,1,1,0,0,1,1,1,0
1,0,1,1,0,0,1,1,0,0
1,0,1,1,0,0,1,0,1,0
1,0,1,1,0,0,1,0,0,1
1,0,1,1,0,0,0,1,1,1
1,0,1,1,0,0,0,1,0,0
1,0,1,1,0,0,0,0,1,0
1,0,1,1,0,0,0,0,0,0
1,0,1,0,1,1,1,1,1,1
1,0,1,0,1,1,1,1,0,0
1,0,1,0,1,1,1,0,1,1
1,0,1,0,1,1,1,0,0,1
1,0,1,0,1,1,0,1,1,0
1,0,1,0,1,1,0,1,0,0
1,0,1,0,1,1,0,0,1,1
1,0,1,0,1,1,0,0,0,0
1,0,1,0,1,0,1,1,1,1
1,0,1,0,1,0,1,1,0,1
1,0,1,0,1,0,1,0,1,0
1,0,1,0,1,0,1,0,0,0
1,0,1,0,1,0,0,1,1,1
1,0,1,0,1,0,0,1,0,0
1,0,1,0,1,0,0,0,1,0
1,0,1,0,1,0,0,0,0,0
1,0,1,0,0,1,1,1,1,0
1,0,1,0,0,1,1,1,0,1
1,0,1,0,0,1,1,0,1,0
1,0,1,0,0,1,1,0,0,0
1,0,1,0,0,1,0,1,1,0
1,0,1,0,0,1,0,1,0,0
1,0,1,0,0,1,0,0,1,1
1,0,1,0,0,1,0,0,0,0
1,0,1,0,0,0,1,1,1,0
1,0,1,0,0,0,1,1,0,0
1,0,1,0,0,0,1,0,1,0
1,0,1,0,0,0,1,0,0,1
1,0,1,0,0,0,0,1,1,0
1,0,1,0,0,0,0,1,0,0
1,0,1,0,0,0,0,0,1,1
1,0,1,0,0,0,0,0,0,1
1,0,0,1,1,1,1,1,1,1
1,0,0,1,1,1,1,1,0,0
1,0,0,1,1,1,1,0,1,1
1,0,0,1,1,1,1,0,0,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,1,1,0,1,0,0
1,0,0,1,1,1,0,0,1,0
1,0,0,1,1,1,0,0,0,0
1,0,0,1,1,0,1,1,1,0
1,0,0,1,1,0,1,1,0,0
1,0,0,1,1,0,1,0,1,1
1,0,0,1,1,0,1,0,0,0
1,0,0,1,1,0,0,1,1,0
1,0,0,1,1,0,0,1,0,0
1,0,0,1,1,0,0,0,1,0
1,0,0,1,1,0,0,0,0,1
1,0,0,1,0,1,1,1,1,0
1,0,0,1,0,1,1,1,0,1
1,0,0,1,0,1,1,0,1,0
1,0,0,1,0,1,1,0,0,0
1,0,0,1,0,1,0,1,1,0
1,0,0,1,0,1,0,1,0,1
1,0,0,1,0,1,0,0,1,0
1,0,0,1,0,1,0,0,0,0
1,0,0,1,0,0,1,1,1,0
1,0,0,1,0,0,1,1,0,0
1,0,0,1,0,0,1,0,1,1
1,0,0,1,0,0,1,0,0,0
1,0,0,1,0,0,0,1,1,0
1,0,0,1,0,0,0,1,0,0
1,0,0,1,0,0,0,0,1,0
1,0,0,1,0,0,0,0,0,0
1,0,0,0,1,1,1,1,1,0
1,0,0,0,1,1,1,1,0,0
1,0,0,0,1,1,1,0,1,1
1,0,0,0,1,1,1,0,0,0
1,0,0,0,1,1,0,1,1,1
1,0,0,0,1,1,0,1,0,0
1,0,0,0,1,1,0,0,1,0
1,0,0,0,1,1,0,0,0,0
1,0,0,0,1,0,1,1,1,1
1,0,0,0,1,0,1,1,0,0
1,0,0,0,1,0,1,0,1,0
1,0,0,0,1,0,1,0,0,0
1,0,0,0,1,0,0,1,1,0
1,0,0,0,1,0,0,1,0,0
1,0,0,0,1,0,0,0,1,1
1,0,0,0,1,0,0,0,0,1
1,0,0,0,0,1,1,1,1,0
1,0,0,0,0,1,1,1,0,0
1,0,0,0,0,1,1,0,1,0
1,0,0,0,0,1,1,0,0,0
1,0,0,0,0,1,0,1,1,0
1,0,0,0,0,1,0,1,0,0
1,0,0,0,0,1,0,0,1,0
1,0,0,0,0,1,0,0,0,0
1,0,0,0,0,0,1,1,1,1
1,0,0,0,0,0,1,1,0,0
1,0,0,0,0,0,1,0,1,1
1,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,0,1,1,0
1,0,0,0,0,0,0,1,0,0
1,0,0,0,0,0,0,0,1,0
1,0,0,0,0,0,0,0,0,0
0,1,1,1,1,1,1,1,1,0
0,1,1,1,1,1,1,1,0,0
0,1,1,1,1,1,1,0,1,0
0,1,1,1,1,1,1,0,0,0
0,1,1,1,1,1,0,1,1,0
0,1,1,1,1,1,0,1,0,0
0,1,1,1,1,1,0,0,1,0
0,1,1,1,1,1,0,0,0,0
0,1,1,1,1,0,1,1,1,0
0,1,1,1,1,0,1,1,0,0
0,1,1,1,1,0,1,0,1,0
0,1,1,1,1,0,1,0,0,0
0,1,1,1,1,0,0,1,1,0
0,1,1,1,1,0,0,1,0,0
0,1,1,1,1,0,0,0,1,0
0,1,1,1,1,0,0,0,0,0
0,1,1,1,0,1,1,1,1,0
0,1,1,1,0,1,1,1,0,0
0,1,1,1,0,1,1,0,1,0
0,1,1,1,0,1,1,0,0,0
0,1,1,1,0,1,0,1,1,0
0,1,1,1,0,1,0,1,0,0
0,1,1,1,0,1,0,0,1,1
0,1,1,1,0,1,0,0,0,1
0,1,1,1,0,0,1,1,1,0
0,1,1,1,0,0,1,1,0,0
0,1,1,1,0,0,1,0,1,1
0,1,1,1,0,0,1,0,0,0
0,1,1,1,0,0,0,1,1,0
0,1,1,1,0,0,0,1,0,1
0,1,1,1,0,0,0,0,1,0
0,1,1,1,0,0,0,0,0,0
0,1,1,0,1,1,1,1,1,1
0,1,1,0,1,1,1,1,0,0
0,1,1,0,1,1,1,0,1,0
0,1,1,0,1,1,1,0,0,1
0,1,1,0,1,1,0,1,1,0
0,1,1,0,1,1,0,1,0,0
0,1,1,0,1,1,0,0,1,0
0,1,1,0,1,1,0,0,0,0
0,1,1,0,1,0,1,1,1,1
0,1,1,0,1,0,1,1,0,0
0,1,1,0,1,0,1,0,1,1
0,1,1,0,1,0,1,0,0,0
0,1,1,0,1,0,0,1,1,0
0,1,1,0,1,0,0,1,0,0
0,1,1,0,1,0,0,0,1,0
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,1,1,1,0
0,1,1,0,0,1,1,1,0,0
0,1,1,0,0,1,1,0,1,0
0,1,1,0,0,1,1,0,0,0
0,1,1,0,0,1,0,1,1,1
0,1,1,0,0,1,0,1,0,1
0,1,1,0,0,1,0,0,1,0
0,1,1,0,0,1,0,0,0,0
0,1,1,0,0,0,1,1,1,0
0,1,1,0,0,0,1,1,0,0
0,1,1,0,0,0,1,0,1,0
0,1,1,0,0,0,1,0,0,0
0,1,1,0,0,0,0,1,1,0
0,1,1,0,0,0,0,1,0,0
0,1,1,0,0,0,0,0,1,0
0,1,1,0,0,0,0,0,0,0
0,1,0,1,1,1,1,1,1,0
0,1,0,1,1,1,1,1,0,0
0,1,0,1,1,1,1,0,1,0
0,1,0,1,1,1,1,0,0,0
0,1,0,1,1,1,0,1,1,0
0,1,0,1,1,1,0,1,0,0
0,1,0,1,1,1,0,0,1,0
0,1,0,1,1,1,0,0,0,0
0,1,0,1,1,0,1,1,1,0
0,1,0,1,1,0,1,1,0,0
0,1,0,1,1,0,1,0,1,0
0,1,0,1,1,0,1,0,0,0
0,1,0,1,1,0,0,1,1,0
0,1,0,1,1,0,0,1,0,0
0,1,0,1,1,0,0,0,1,0
0,1,0,1,1,0,0,0,0,1
0,1,0,1,0,1,1,1,1,0
0,1,0,1,0,1,1,1,0,0
0,1,0,1,0,1,1,0,1,0
0,1,0,1,0,1,1,0,0,1
0,1,0,1,0,1,0,1,1,0
0,1,0,1,0,1,0,1,0,0
0,1,0,1,0,1,0,0,1,1
0,1,0,1,0,1,0,0,0,0
0,1,0,1,0,0,1,1,1,1
0,1,0,1,0,0,1,1,0,1
0,1,0,1,0,0,1,0,1,0
0,1,0,1,0,0,1,0,0,0
0,1,0,1,0,0,0,1,1,1
0,1,0,1,0,0,0,1,0,0
0,1,0,1,0,0,0,0,1,0
0,1,0,1,0,0,0,0,0,1
0,1,0,0,1,1,1,1,1,0
0,1,0,0,1,1,1,1,0,0
0,1,0,0,1,1,1,0,1,0
0,1,0,0,1,1,1,0,0,0
0,1,0,0,1,1,0,1,1,0
0,1,0,0,1,1,0,1,0,0
0,1,0,0,1,1,0,0,1,0
0,1,0,0,1,1,0,0,0,1
0,1,0,0,1,0,1,1,1,0
0,1,0,0,1,0,1,1,0,0
0,1,0,0,1,0,1,0,1,0
0,1,0,0,1,0,1,0,0,0
0,1,0,0,1,0,0,1,1,0
0,1,0,0,1,0,0,1,0,0
0,1,0,0,1,0,0,0,1,0
0,1,0,0,1,0,0,0,0,1
0,1,0,0,0,1,1,1,1,1
0,1,0,0,0,1,1,1,0,1
0,1,0,0,0,1,1,0,1,0
0,1,0,0,0,1,1,0,0,0
0,1,0,0,0,1,0,1,1,1
0,1,0,0,0,1,0,1,0,0
0,1,0,0,0,1,0,0,1,0
0,1,0,0,0,1,0,0,0,1
0,1,0,0,0,0,1,1,1,0
0,1,0,0,0,0,1,1,0,0
0,1,0,0,0,0,1,0,1,0
0,1,0,0,0,0,1,0,0,0
0,1,0,0,0,0,0,1,1,0
0,1,0,0,0,0,0,1,0,1
0,1,0,0,0,0,0,0,1,0
0,1,0,0,0,0,0,0,0,0
0,0,1,1,1,1,1,1,1,1
0,0,1,1,1,1,1,1,0,0
0,0,1,1,1,1,1,0,1,1
0,0,1,1,1,1,1,0,0,0
0,0,1,1,1,1,0,1,1,0
0,0,1,1,1,1,0,1,0,0
0,0,1,1,1,1,0,0,1,0
0,0,1,1,1,1,0,0,0,0
0,0,1,1,1,0,1,1,1,0
0,0,1,1,1,0,1,1,0,1
0,0,1,1,1,0,1,0,1,1
0,0,1,1,1,0,1,0,0,0
0,0,1,1,1,0,0,1,1,0
0,0,1,1,1,0,0,1,0,0
0,0,1,1,1,0,0,0,1,0
0,0,1,1,1,0,0,0,0,0
0,0,1,1,0,1,1,1,1,0
0,0,1,1,0,1,1,1,0,0
0,0,1,1,0,1,1,0,1,0
0,0,1,1,0,1,1,0,0,0
0,0,1,1,0,1,0,1,1,1
0,0,1,1,0,1,0,1,0,1
0,0,1,1,0,1,0,0,1,0
0,0,1,1,0,1,0,0,0,0
0,0,1,1,0,0,1,1,1,0
0,0,1,1,0,0,1,1,0,0
0,0,1,1,0,0,1,0,1,0
0,0,1,1,0,0,1,0,0,0
0,0,1,1,0,0,0,1,1,0
0,0,1,1,0,0,0,1,0,0
0,0,1,1,0,0,0,0,1,0
0,0,1,1,0,0,0,0,0,0
0,0,1,0,1,1,1,1,1,0
0,0,1,0,1,1,1,1,0,0
0,0,1,0,1,1,1,0,1,1
0,0,1,0,1,1,1,0,0,0
0,0,1,0,1,1,0,1,1,0
0,0,1,0,1,1,0,1,0,0
0,0,1,0,1,1,0,0,1,0
0,0,1,0,1,1,0,0,0,1
0,0,1,0,1,0,1,1,1,1
0,0,1,0,1,0,1,1,0,0
0,0,1,0,1,0,1,0,1,0
0,0,1,0,1,0,1,0,0,1
0,0,1,0,1,0,0,1,1,0
0,0,1,0,1,0,0,1,0,0
0,0,1,0,1,0,0,0,1,0
0,0,1,0,1,0,0,0,0,1
0,0,1,0,0,1,1,1,1,0
0,0,1,0,0,1,1,1,0,0
0,0,1,0,0,1,1,0,1,1
0,0,1,0,0,1,1,0,0,0
0,0,1,0,0,1,0,1,1,0
0,0,1,0,0,1,0,1,0,0
0,0,1,0,0,1,0,0,1,0
0,0,1,0,0,1,0,0,0,0
0,0,1,0,0,0,1,1,1,1
0,0,1,0,0,0,1,1,0,0
0,0,1,0,0,0,1,0,1,1
0,0,1,0,0,0,1,0,0,0
0,0,1,0,0,0,0,1,1,0
0,0,1,0,0,0,0,1,0,0
0,0,1,0,0,0,0,0,1,1
0,0,1,0,0,0,0,0,0,0
0,0,0,1,1,1,1,1,1,0
0,0,0,1,1,1,1,1,0,0
0,0,0,1,1,1,1,0,1,1
0,0,0,1,1,1,1,0,0,0
0,0,0,1,1,1,0,1,1,0
0,0,0,1,1,1,0,1,0,0
0,0,0,1,1,1,0,0,1,0
0,0,0,1,1,1,0,0,0,0
0,0,0,1,1,0,1,1,1,0
0,0,0,1,1,0,1,1,0,0
0,0,0,1,1,0,1,0,1,0
0,0,0,1,1,0,1,0,0,1
0,0,0,1,1,0,0,1,1,0
0,0,0,1,1,0,0,1,0,1
0,0,0,1,1,0,0,0,1,0
0,0,0,1,1,0,0,0,0,1
0,0,0,1,0,1,1,1,1,1
0,0,0,1,0,1,1,1,0,1
0,0,0,1,0,1,1,0,1,0
0,0,0,1,0,1,1,0,0,0
0,0,0,1,0,1,0,1,1,1
0,0,0,1,0,1,0,1,0,0
0,0,0,1,0,1,0,0,1,0
0,0,0,1,0,1,0,0,0,1
0,0,0,1,0,0,1,1,1,0
0,0,0,1,0,0,1,1,0,0
0,0,0,1,0,0,1,0,1,0
0,0,0,1,0,0,1,0,0,0
0,0,0,1,0,0,0,1,1,0
0,0,0,1,0,0,0,1,0,1
0,0,0,1,0,0,0,0,1,0
0,0,0,1,0,0,0,0,0,0
0,0,0,0,1,1,1,1,1,0
0,0,0,0,1,1,1,1,0,0
0,0,0,0,1,1,1,0,1,0
0,0,0,0,1,1,1,0,0,0
0,0,0,0,1,1,0,1,1,0
0,0,0,0,1,1,0,1,0,1
0,0,0,0,1,1,0,0,1,1
0,0,0,0,1,1,0,0,0,1
0,0,0,0,1,0,1,1,1,0
0,0,0,0,1,0,1,1,0,1
0,0,0,0,1,0,1,0,1,0
0,0,0,0,1,0,1,0,0,1
0,0,0,0,1,0,0,1,1,1
0,0,0,0,1,0,0,1,0,1
0,0,0,0,1,0,0,0,1,1
0,0,0,0,1,0,0,0,0,0
0,0,0,0,0,1,1,1,1,0
0,0,0,0,0,1,1,1,0,0
0,0,0,0,0,1,1,0,1,0
0,0,0,0,0,1,1,0,0,0
0,0,0,0,0,1,0,1,1,0
0,0,0,0,0,1,0,1,0,1
0,0,0,0,0,1,0,0,1,0
0,0,0,0,0,1,0,0,0,0
0,0,0,0,0,0,1,1,1,1
0,0,0,0,0,0,1,1,0,0
0,0,0,0,0,0,1,0,1,1
0,0,0,0,0,0,1,0,0,0
0,0,0,0,0,0,0,1,1,0
0,0,0,0,0,0,0,1,0,0
0,0,0,0,0,0,0,0,1,0
0,0,0,0,0,0,0,0,0,0

(note that this is unoptimized in a number of ways; for instance, 'stay-the-same' - 0->0 or 1->1 - transitions don't need to be specified, and there are ways of using variables to shrink the table's size)

Code: Select all

x = 43, y = 11, rule = not-x-rule
9b2o2b2o3b2o$8bo4b2o2bob2o5$3bo7b2o4bo23b2o$2bo7bo5bo8b2o5bo7bo$23bob
2o4bo$b2o6b2o4b2o5bo3bo4bo3bo5b2o$o7bo6b2o5bo11bo6bo!

When that didn't work, I tried reversing the order - counting up from 000000000 to 111111111. Still nothing.

Code: Select all

@RULE also-not-x-rule
@TABLE

n_states:2
neighborhood:Moore
symmetries:none

0,0,0,0,0,0,0,0,0,0
1,0,0,0,0,0,0,0,0,0
0,1,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,1
0,0,1,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
0,1,1,0,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,0
0,0,0,1,0,0,0,0,0,0
1,0,0,1,0,0,0,0,0,1
0,1,0,1,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,0
0,0,1,1,0,0,0,0,0,0
1,0,1,1,0,0,0,0,0,0
0,1,1,1,0,0,0,0,0,0
1,1,1,1,0,0,0,0,0,0
0,0,0,0,1,0,0,0,0,0
1,0,0,0,1,0,0,0,0,0
0,1,0,0,1,0,0,0,0,0
1,1,0,0,1,0,0,0,0,0
0,0,1,0,1,0,0,0,0,0
1,0,1,0,1,0,0,0,0,0
0,1,1,0,1,0,0,0,0,0
1,1,1,0,1,0,0,0,0,1
0,0,0,1,1,0,0,0,0,0
1,0,0,1,1,0,0,0,0,0
0,1,0,1,1,0,0,0,0,0
1,1,0,1,1,0,0,0,0,0
0,0,1,1,1,0,0,0,0,0
1,0,1,1,1,0,0,0,0,1
0,1,1,1,1,0,0,0,0,0
1,1,1,1,1,0,0,0,0,0
0,0,0,0,0,1,0,0,0,0
1,0,0,0,0,1,0,0,0,0
0,1,0,0,0,1,0,0,0,1
1,1,0,0,0,1,0,0,0,0
0,0,1,0,0,1,0,0,0,1
1,0,1,0,0,1,0,0,0,0
0,1,1,0,0,1,0,0,0,0
1,1,1,0,0,1,0,0,0,0
0,0,0,1,0,1,0,0,0,0
1,0,0,1,0,1,0,0,0,1
0,1,0,1,0,1,0,0,0,1
1,1,0,1,0,1,0,0,0,1
0,0,1,1,0,1,0,0,0,1
1,0,1,1,0,1,0,0,0,0
0,1,1,1,0,1,0,0,0,1
1,1,1,1,0,1,0,0,0,0
0,0,0,0,1,1,0,0,0,0
1,0,0,0,1,1,0,0,0,0
0,1,0,0,1,1,0,0,0,0
1,1,0,0,1,1,0,0,0,0
0,0,1,0,1,1,0,0,0,0
1,0,1,0,1,1,0,0,0,1
0,1,1,0,1,1,0,0,0,0
1,1,1,0,1,1,0,0,0,0
0,0,0,1,1,1,0,0,0,0
1,0,0,1,1,1,0,0,0,0
0,1,0,1,1,1,0,0,0,0
1,1,0,1,1,1,0,0,0,1
0,0,1,1,1,1,0,0,0,0
1,0,1,1,1,1,0,0,0,0
0,1,1,1,1,1,0,0,0,1
1,1,1,1,1,1,0,0,0,1
0,0,0,0,0,0,1,0,0,0
1,0,0,0,0,0,1,0,0,0
0,1,0,0,0,0,1,0,0,0
1,1,0,0,0,0,1,0,0,0
0,0,1,0,0,0,1,0,0,0
1,0,1,0,0,0,1,0,0,0
0,1,1,0,0,0,1,0,0,0
1,1,1,0,0,0,1,0,0,0
0,0,0,1,0,0,1,0,0,1
1,0,0,1,0,0,1,0,0,0
0,1,0,1,0,0,1,0,0,0
1,1,0,1,0,0,1,0,0,0
0,0,1,1,0,0,1,0,0,0
1,0,1,1,0,0,1,0,0,0
0,1,1,1,0,0,1,0,0,1
1,1,1,1,0,0,1,0,0,0
0,0,0,0,1,0,1,0,0,0
1,0,0,0,1,0,1,0,0,0
0,1,0,0,1,0,1,0,0,0
1,1,0,0,1,0,1,0,0,1
0,0,1,0,1,0,1,0,0,0
1,0,1,0,1,0,1,0,0,0
0,1,1,0,1,0,1,0,0,0
1,1,1,0,1,0,1,0,0,1
0,0,0,1,1,0,1,0,0,0
1,0,0,1,1,0,1,0,0,0
0,1,0,1,1,0,1,0,0,0
1,1,0,1,1,0,1,0,0,0
0,0,1,1,1,0,1,0,0,0
1,0,1,1,1,0,1,0,0,1
0,1,1,1,1,0,1,0,0,0
1,1,1,1,1,0,1,0,0,0
0,0,0,0,0,1,1,0,0,0
1,0,0,0,0,1,1,0,0,0
0,1,0,0,0,1,1,0,0,0
1,1,0,0,0,1,1,0,0,0
0,0,1,0,0,1,1,0,0,0
1,0,1,0,0,1,1,0,0,0
0,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,1,0,0,0
0,0,0,1,0,1,1,0,0,1
1,0,0,1,0,1,1,0,0,0
0,1,0,1,0,1,1,0,0,1
1,1,0,1,0,1,1,0,0,0
0,0,1,1,0,1,1,0,0,0
1,0,1,1,0,1,1,0,0,0
0,1,1,1,0,1,1,0,0,0
1,1,1,1,0,1,1,0,0,1
0,0,0,0,1,1,1,0,0,0
1,0,0,0,1,1,1,0,0,0
0,1,0,0,1,1,1,0,0,1
1,1,0,0,1,1,1,0,0,0
0,0,1,0,1,1,1,0,0,0
1,0,1,0,1,1,1,0,0,1
0,1,1,0,1,1,1,0,0,0
1,1,1,0,1,1,1,0,0,0
0,0,0,1,1,1,1,0,0,0
1,0,0,1,1,1,1,0,0,0
0,1,0,1,1,1,1,0,0,0
1,1,0,1,1,1,1,0,0,0
0,0,1,1,1,1,1,0,0,0
1,0,1,1,1,1,1,0,0,0
0,1,1,1,1,1,1,0,0,0
1,1,1,1,1,1,1,0,0,0
0,0,0,0,0,0,0,1,0,0
1,0,0,0,0,0,0,1,0,0
0,1,0,0,0,0,0,1,0,0
1,1,0,0,0,0,0,1,0,1
0,0,1,0,0,0,0,1,0,0
1,0,1,0,0,0,0,1,0,0
0,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,1,0,1
0,0,0,1,0,0,0,1,0,1
1,0,0,1,0,0,0,1,0,0
0,1,0,1,0,0,0,1,0,1
1,1,0,1,0,0,0,1,0,1
0,0,1,1,0,0,0,1,0,0
1,0,1,1,0,0,0,1,0,0
0,1,1,1,0,0,0,1,0,1
1,1,1,1,0,0,0,1,0,0
0,0,0,0,1,0,0,1,0,0
1,0,0,0,1,0,0,1,0,0
0,1,0,0,1,0,0,1,0,0
1,1,0,0,1,0,0,1,0,0
0,0,1,0,1,0,0,1,0,0
1,0,1,0,1,0,0,1,0,0
0,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,1,0,0
0,0,0,1,1,0,0,1,0,0
1,0,0,1,1,0,0,1,0,0
0,1,0,1,1,0,0,1,0,0
1,1,0,1,1,0,0,1,0,1
0,0,1,1,1,0,0,1,0,1
1,0,1,1,1,0,0,1,0,0
0,1,1,1,1,0,0,1,0,0
1,1,1,1,1,0,0,1,0,0
0,0,0,0,0,1,0,1,0,1
1,0,0,0,0,1,0,1,0,0
0,1,0,0,0,1,0,1,0,1
1,1,0,0,0,1,0,1,0,1
0,0,1,0,0,1,0,1,0,0
1,0,1,0,0,1,0,1,0,0
0,1,1,0,0,1,0,1,0,1
1,1,1,0,0,1,0,1,0,0
0,0,0,1,0,1,0,1,0,1
1,0,0,1,0,1,0,1,0,1
0,1,0,1,0,1,0,1,0,0
1,1,0,1,0,1,0,1,0,0
0,0,1,1,0,1,0,1,0,1
1,0,1,1,0,1,0,1,0,0
0,1,1,1,0,1,0,1,0,0
1,1,1,1,0,1,0,1,0,0
0,0,0,0,1,1,0,1,0,0
1,0,0,0,1,1,0,1,0,1
0,1,0,0,1,1,0,1,0,0
1,1,0,0,1,1,0,1,0,0
0,0,1,0,1,1,0,1,0,0
1,0,1,0,1,1,0,1,0,0
0,1,1,0,1,1,0,1,0,1
1,1,1,0,1,1,0,1,0,0
0,0,0,1,1,1,0,1,0,0
1,0,0,1,1,1,0,1,0,0
0,1,0,1,1,1,0,1,0,0
1,1,0,1,1,1,0,1,0,1
0,0,1,1,1,1,0,1,0,0
1,0,1,1,1,1,0,1,0,0
0,1,1,1,1,1,0,1,0,1
1,1,1,1,1,1,0,1,0,1
0,0,0,0,0,0,1,1,0,1
1,0,0,0,0,0,1,1,0,0
0,1,0,0,0,0,1,1,0,1
1,1,0,0,0,0,1,1,0,0
0,0,1,0,0,0,1,1,0,0
1,0,1,0,0,0,1,1,0,0
0,1,1,0,0,0,1,1,0,0
1,1,1,0,0,0,1,1,0,0
0,0,0,1,0,0,1,1,0,0
1,0,0,1,0,0,1,1,0,0
0,1,0,1,0,0,1,1,0,1
1,1,0,1,0,0,1,1,0,0
0,0,1,1,0,0,1,1,0,0
1,0,1,1,0,0,1,1,0,0
0,1,1,1,0,0,1,1,0,0
1,1,1,1,0,0,1,1,0,1
0,0,0,0,1,0,1,1,0,0
1,0,0,0,1,0,1,1,0,1
0,1,0,0,1,0,1,1,0,0
1,1,0,0,1,0,1,1,0,0
0,0,1,0,1,0,1,1,0,0
1,0,1,0,1,0,1,1,0,1
0,1,1,0,1,0,1,1,0,0
1,1,1,0,1,0,1,1,0,0
0,0,0,1,1,0,1,1,0,0
1,0,0,1,1,0,1,1,0,0
0,1,0,1,1,0,1,1,0,1
1,1,0,1,1,0,1,1,0,0
0,0,1,1,1,0,1,1,0,0
1,0,1,1,1,0,1,1,0,0
0,1,1,1,1,0,1,1,0,0
1,1,1,1,1,0,1,1,0,0
0,0,0,0,0,1,1,1,0,0
1,0,0,0,0,1,1,1,0,0
0,1,0,0,0,1,1,1,0,1
1,1,0,0,0,1,1,1,0,0
0,0,1,0,0,1,1,1,0,1
1,0,1,0,0,1,1,1,0,0
0,1,1,0,0,1,1,1,0,0
1,1,1,0,0,1,1,1,0,0
0,0,0,1,0,1,1,1,0,1
1,0,0,1,0,1,1,1,0,0
0,1,0,1,0,1,1,1,0,0
1,1,0,1,0,1,1,1,0,0
0,0,1,1,0,1,1,1,0,0
1,0,1,1,0,1,1,1,0,0
0,1,1,1,0,1,1,1,0,1
1,1,1,1,0,1,1,1,0,1
0,0,0,0,1,1,1,1,0,0
1,0,0,0,1,1,1,1,0,0
0,1,0,0,1,1,1,1,0,0
1,1,0,0,1,1,1,1,0,0
0,0,1,0,1,1,1,1,0,0
1,0,1,0,1,1,1,1,0,0
0,1,1,0,1,1,1,1,0,0
1,1,1,0,1,1,1,1,0,0
0,0,0,1,1,1,1,1,0,1
1,0,0,1,1,1,1,1,0,0
0,1,0,1,1,1,1,1,0,1
1,1,0,1,1,1,1,1,0,1
0,0,1,1,1,1,1,1,0,0
1,0,1,1,1,1,1,1,0,0
0,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1,0,0
0,0,0,0,0,0,0,0,1,0
1,0,0,0,0,0,0,0,1,0
0,1,0,0,0,0,0,0,1,0
1,1,0,0,0,0,0,0,1,0
0,0,1,0,0,0,0,0,1,0
1,0,1,0,0,0,0,0,1,0
0,1,1,0,0,0,0,0,1,0
1,1,1,0,0,0,0,0,1,0
0,0,0,1,0,0,0,0,1,0
1,0,0,1,0,0,0,0,1,0
0,1,0,1,0,0,0,0,1,0
1,1,0,1,0,0,0,0,1,0
0,0,1,1,0,0,0,0,1,0
1,0,1,1,0,0,0,0,1,0
0,1,1,1,0,0,0,0,1,0
1,1,1,1,0,0,0,0,1,0
0,0,0,0,1,0,0,0,1,0
1,0,0,0,1,0,0,0,1,0
0,1,0,0,1,0,0,0,1,0
1,1,0,0,1,0,0,0,1,0
0,0,1,0,1,0,0,0,1,0
1,0,1,0,1,0,0,0,1,0
0,1,1,0,1,0,0,0,1,1
1,1,1,0,1,0,0,0,1,1
0,0,0,1,1,0,0,0,1,0
1,0,0,1,1,0,0,0,1,0
0,1,0,1,1,0,0,0,1,1
1,1,0,1,1,0,0,0,1,0
0,0,1,1,1,0,0,0,1,0
1,0,1,1,1,0,0,0,1,1
0,1,1,1,1,0,0,0,1,0
1,1,1,1,1,0,0,0,1,0
0,0,0,0,0,1,0,0,1,1
1,0,0,0,0,1,0,0,1,0
0,1,0,0,0,1,0,0,1,0
1,1,0,0,0,1,0,0,1,1
0,0,1,0,0,1,0,0,1,0
1,0,1,0,0,1,0,0,1,0
0,1,1,0,0,1,0,0,1,0
1,1,1,0,0,1,0,0,1,0
0,0,0,1,0,1,0,0,1,1
1,0,0,1,0,1,0,0,1,0
0,1,0,1,0,1,0,0,1,1
1,1,0,1,0,1,0,0,1,0
0,0,1,1,0,1,0,0,1,0
1,0,1,1,0,1,0,0,1,0
0,1,1,1,0,1,0,0,1,0
1,1,1,1,0,1,0,0,1,1
0,0,0,0,1,1,0,0,1,0
1,0,0,0,1,1,0,0,1,0
0,1,0,0,1,1,0,0,1,0
1,1,0,0,1,1,0,0,1,0
0,0,1,0,1,1,0,0,1,1
1,0,1,0,1,1,0,0,1,1
0,1,1,0,1,1,0,0,1,0
1,1,1,0,1,1,0,0,1,0
0,0,0,1,1,1,0,0,1,0
1,0,0,1,1,1,0,0,1,0
0,1,0,1,1,1,0,0,1,0
1,1,0,1,1,1,0,0,1,0
0,0,1,1,1,1,0,0,1,0
1,0,1,1,1,1,0,0,1,0
0,1,1,1,1,1,0,0,1,0
1,1,1,1,1,1,0,0,1,0
0,0,0,0,0,0,1,0,1,0
1,0,0,0,0,0,1,0,1,0
0,1,0,0,0,0,1,0,1,0
1,1,0,0,0,0,1,0,1,0
0,0,1,0,0,0,1,0,1,0
1,0,1,0,0,0,1,0,1,0
0,1,1,0,0,0,1,0,1,0
1,1,1,0,0,0,1,0,1,0
0,0,0,1,0,0,1,0,1,0
1,0,0,1,0,0,1,0,1,0
0,1,0,1,0,0,1,0,1,0
1,1,0,1,0,0,1,0,1,0
0,0,1,1,0,0,1,0,1,0
1,0,1,1,0,0,1,0,1,0
0,1,1,1,0,0,1,0,1,0
1,1,1,1,0,0,1,0,1,1
0,0,0,0,1,0,1,0,1,0
1,0,0,0,1,0,1,0,1,0
0,1,0,0,1,0,1,0,1,0
1,1,0,0,1,0,1,0,1,1
0,0,1,0,1,0,1,0,1,0
1,0,1,0,1,0,1,0,1,0
0,1,1,0,1,0,1,0,1,1
1,1,1,0,1,0,1,0,1,0
0,0,0,1,1,0,1,0,1,1
1,0,0,1,1,0,1,0,1,1
0,1,0,1,1,0,1,0,1,0
1,1,0,1,1,0,1,0,1,0
0,0,1,1,1,0,1,0,1,1
1,0,1,1,1,0,1,0,1,0
0,1,1,1,1,0,1,0,1,0
1,1,1,1,1,0,1,0,1,1
0,0,0,0,0,1,1,0,1,0
1,0,0,0,0,1,1,0,1,0
0,1,0,0,0,1,1,0,1,0
1,1,0,0,0,1,1,0,1,0
0,0,1,0,0,1,1,0,1,0
1,0,1,0,0,1,1,0,1,0
0,1,1,0,0,1,1,0,1,0
1,1,1,0,0,1,1,0,1,1
0,0,0,1,0,1,1,0,1,0
1,0,0,1,0,1,1,0,1,0
0,1,0,1,0,1,1,0,1,0
1,1,0,1,0,1,1,0,1,0
0,0,1,1,0,1,1,0,1,0
1,0,1,1,0,1,1,0,1,0
0,1,1,1,0,1,1,0,1,0
1,1,1,1,0,1,1,0,1,1
0,0,0,0,1,1,1,0,1,1
1,0,0,0,1,1,1,0,1,1
0,1,0,0,1,1,1,0,1,0
1,1,0,0,1,1,1,0,1,0
0,0,1,0,1,1,1,0,1,1
1,0,1,0,1,1,1,0,1,0
0,1,1,0,1,1,1,0,1,0
1,1,1,0,1,1,1,0,1,1
0,0,0,1,1,1,1,0,1,0
1,0,0,1,1,1,1,0,1,0
0,1,0,1,1,1,1,0,1,0
1,1,0,1,1,1,1,0,1,0
0,0,1,1,1,1,1,0,1,0
1,0,1,1,1,1,1,0,1,1
0,1,1,1,1,1,1,0,1,0
1,1,1,1,1,1,1,0,1,0
0,0,0,0,0,0,0,1,1,1
1,0,0,0,0,0,0,1,1,0
0,1,0,0,0,0,0,1,1,1
1,1,0,0,0,0,0,1,1,0
0,0,1,0,0,0,0,1,1,0
1,0,1,0,0,0,0,1,1,0
0,1,1,0,0,0,0,1,1,0
1,1,1,0,0,0,0,1,1,0
0,0,0,1,0,0,0,1,1,0
1,0,0,1,0,0,0,1,1,1
0,1,0,1,0,0,0,1,1,1
1,1,0,1,0,0,0,1,1,0
0,0,1,1,0,0,0,1,1,0
1,0,1,1,0,0,0,1,1,0
0,1,1,1,0,0,0,1,1,0
1,1,1,1,0,0,0,1,1,0
0,0,0,0,1,0,0,1,1,0
1,0,0,0,1,0,0,1,1,0
0,1,0,0,1,0,0,1,1,0
1,1,0,0,1,0,0,1,1,0
0,0,1,0,1,0,0,1,1,1
1,0,1,0,1,0,0,1,1,1
0,1,1,0,1,0,0,1,1,0
1,1,1,0,1,0,0,1,1,0
0,0,0,1,1,0,0,1,1,0
1,0,0,1,1,0,0,1,1,0
0,1,0,1,1,0,0,1,1,0
1,1,0,1,1,0,0,1,1,0
0,0,1,1,1,0,0,1,1,0
1,0,1,1,1,0,0,1,1,0
0,1,1,1,1,0,0,1,1,0
1,1,1,1,1,0,0,1,1,0
0,0,0,0,0,1,0,1,1,0
1,0,0,0,0,1,0,1,1,0
0,1,0,0,0,1,0,1,1,1
1,1,0,0,0,1,0,1,1,0
0,0,1,0,0,1,0,1,1,0
1,0,1,0,0,1,0,1,1,0
0,1,1,0,0,1,0,1,1,0
1,1,1,0,0,1,0,1,1,1
0,0,0,1,0,1,0,1,1,1
1,0,0,1,0,1,0,1,1,0
0,1,0,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,1,1
0,0,1,1,0,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
0,1,1,1,0,1,0,1,1,0
1,1,1,1,0,1,0,1,1,1
0,0,0,0,1,1,0,1,1,0
1,0,0,0,1,1,0,1,1,0
0,1,0,0,1,1,0,1,1,1
1,1,0,0,1,1,0,1,1,0
0,0,1,0,1,1,0,1,1,0
1,0,1,0,1,1,0,1,1,0
0,1,1,0,1,1,0,1,1,0
1,1,1,0,1,1,0,1,1,0
0,0,0,1,1,1,0,1,1,1
1,0,0,1,1,1,0,1,1,0
0,1,0,1,1,1,0,1,1,1
1,1,0,1,1,1,0,1,1,0
0,0,1,1,1,1,0,1,1,0
1,0,1,1,1,1,0,1,1,0
0,1,1,1,1,1,0,1,1,1
1,1,1,1,1,1,0,1,1,0
0,0,0,0,0,0,1,1,1,0
1,0,0,0,0,0,1,1,1,0
0,1,0,0,0,0,1,1,1,1
1,1,0,0,0,0,1,1,1,0
0,0,1,0,0,0,1,1,1,0
1,0,1,0,0,0,1,1,1,0
0,1,1,0,0,0,1,1,1,0
1,1,1,0,0,0,1,1,1,0
0,0,0,1,0,0,1,1,1,0
1,0,0,1,0,0,1,1,1,0
0,1,0,1,0,0,1,1,1,0
1,1,0,1,0,0,1,1,1,1
0,0,1,1,0,0,1,1,1,0
1,0,1,1,0,0,1,1,1,1
0,1,1,1,0,0,1,1,1,0
1,1,1,1,0,0,1,1,1,1
0,0,0,0,1,0,1,1,1,1
1,0,0,0,1,0,1,1,1,1
0,1,0,0,1,0,1,1,1,0
1,1,0,0,1,0,1,1,1,0
0,0,1,0,1,0,1,1,1,1
1,0,1,0,1,0,1,1,1,0
0,1,1,0,1,0,1,1,1,0
1,1,1,0,1,0,1,1,1,1
0,0,0,1,1,0,1,1,1,0
1,0,0,1,1,0,1,1,1,0
0,1,0,1,1,0,1,1,1,0
1,1,0,1,1,0,1,1,1,0
0,0,1,1,1,0,1,1,1,0
1,0,1,1,1,0,1,1,1,1
0,1,1,1,1,0,1,1,1,0
1,1,1,1,1,0,1,1,1,0
0,0,0,0,0,1,1,1,1,0
1,0,0,0,0,1,1,1,1,0
0,1,0,0,0,1,1,1,1,0
1,1,0,0,0,1,1,1,1,0
0,0,1,0,0,1,1,1,1,0
1,0,1,0,0,1,1,1,1,1
0,1,1,0,0,1,1,1,1,1
1,1,1,0,0,1,1,1,1,1
0,0,0,1,0,1,1,1,1,0
1,0,0,1,0,1,1,1,1,1
0,1,0,1,0,1,1,1,1,0
1,1,0,1,0,1,1,1,1,1
0,0,1,1,0,1,1,1,1,1
1,0,1,1,0,1,1,1,1,1
0,1,1,1,0,1,1,1,1,1
1,1,1,1,0,1,1,1,1,0
0,0,0,0,1,1,1,1,1,0
1,0,0,0,1,1,1,1,1,0
0,1,0,0,1,1,1,1,1,0
1,1,0,0,1,1,1,1,1,0
0,0,1,0,1,1,1,1,1,0
1,0,1,0,1,1,1,1,1,1
0,1,1,0,1,1,1,1,1,0
1,1,1,0,1,1,1,1,1,0
0,0,0,1,1,1,1,1,1,1
1,0,0,1,1,1,1,1,1,0
0,1,0,1,1,1,1,1,1,1
1,1,0,1,1,1,1,1,1,0
0,0,1,1,1,1,1,1,1,0
1,0,1,1,1,1,1,1,1,0
0,1,1,1,1,1,1,1,1,0
1,1,1,1,1,1,1,1,1,0

Code: Select all

x = 77, y = 86, rule = also-not-x-rule
31bobobobo$38bo$37b2o$36bo3$37bo$36b2o$27bobobobobo3$31bobobobo$38bo5b
o$37b2o4b2o$28bobobobobo5bo3$43bo$44bo$42bobo$43bo$42b2o$41bo5$46bo$
45b2o$34bobobobobobo2$33bobobobo3bo$40bob2o$33bobobobobo3$41bo$40b2o$
39bo$30bo5bo6bo$32bobo3bobob2o$31bobobobobobo3$39bo$38b2o3$36bobobobo$
43bo$35bo6b2o$36bo4bo$35b2o$34bo10$3bobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobo$72bo3bo$73bob2o$obobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo7$33bo$32b2o
$3bobobobobobobobobobobobobobobo$bo$2bobobobobobobobobobobobobo$27bo$
28bo5bo$29bo3b2o$2bobobobobobobobobobobobobobobobo2$bobobobo$8bo$7b2o!

Any idea what I'm doing wrong?

[dvgrn]

Hm... I tried to make a Golly ruletable for the X-rule based on Figure 12 in the paper, but it didn't quite work out.

I took 'descending order of neighborhood values' to mean counting down, in binary, from 111111111 to 000000000 - where the first digit represents the current cell and the remaining eight represent its Moore neighborhood - matching each row of the image to 64 numbers. (e.g. the first row, 0001001001100000000000010000010000101000011110100000010000010011, went to the neighbor counts 111111111 through 111000000.)
...
Any idea what I'm doing wrong?

It's a good theory. The paper really doesn't explain this well at all -- unless I'm missing seeing a little diagram somewhere that shows which neighbor (or central cell) corresponds to the first bit, which neighbor to the second bit, etc., in 111111111 through 000000000.

There are 512 little squares in that diagram. You must have that part of the mapping right.

But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

There are a few other mappings of bits to neighbors that might make sense, like leftmost bit=center cell, then assign neighbors clockwise from the top center, or from the top left, or just left-to-right then top-to-bottom.

There's an interesting diagonal bilateral symmetry in each of the 8x8 boxes in Figure 12. I assume that corresponds to the rotations and reflections that they talk about, that reduce the space from 2^512 to 2^102.

It should be possible to use those diagonal lines of symmetry to deduce the center/neighbor mapping -- but maybe a little more trial and error will be easier!

[M. I. Wright]

But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

There are a few other mappings of bits to neighbors that might make sense, like leftmost bit=center cell, then assign neighbors clockwise from the top center, or from the top left, or just left-to-right then top-to-bottom.

Whoops, I've gotten used to Golly's rule format! I'd be willing to be that it's your first suggestion, actually.

There's an interesting diagonal bilateral symmetry in each of the 8x8 boxes in Figure 12. I assume that corresponds to the rotations and reflections that they talk about, that reduce the space from 2^512 to 2^102.

It should be possible to use those diagonal lines of symmetry to deduce the center/neighbor mapping -- but maybe a little more trial and error will be easier!

Oh shoot, I completely missed that (both the symmetry in the rule-table and the mention of rotations/reflections - I skimmed over 2.1 at first and didn't see other mentions of symmetry). It might be easier to figure out the rule format (and where the center cell lies in the transition) knowing that the precursor has rotate4reflect symmetry, although I've got nothing for now - I'll wait until jmgomez (hopefully) replies before attempting anything new with the ruletable.

Edit - Alternatively: Is anyone familiar with Mathematica's rule format? The note at the bottom says that X-rule was tested in the language, so it might make sense for the image to correspond with that.

This would also be easier if the website listed - http://www.ddlab.org/Xrule/ - were up...

[dvgrn]

But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

Yup, I think that's got it. Just had to shuffle the bits in the columns of the first rule table, in a very headache-inducing way:

Code: Select all

@RULE x-rule

@TABLE
n_states:2
neighborhood:Moore
symmetries:none

# The first digit represents the current cell, the next eight its Moore neighborhood, and the final digit determines that configuration's output
# C,N,NE,E,SE,S,SW,W,NW,C'
1,1,1,1,1,1,1,1,1,0
1,1,1,1,0,1,1,1,1,0
1,1,1,1,1,0,1,1,1,0
1,1,1,1,0,0,1,1,1,1
1,1,1,1,1,1,0,1,1,0
1,1,1,1,0,1,0,1,1,0
1,1,1,1,1,0,0,1,1,1
1,1,1,1,0,0,0,1,1,0
1,1,1,0,1,1,1,1,1,0
1,1,1,0,0,1,1,1,1,1
1,1,1,0,1,0,1,1,1,1
1,1,1,0,0,0,1,1,1,0
1,1,1,0,1,1,0,1,1,0
1,1,1,0,0,1,0,1,1,0
1,1,1,0,1,0,0,1,1,0
1,1,1,0,0,0,0,1,1,0
0,1,1,1,1,1,1,1,1,0
0,1,1,1,0,1,1,1,1,0
0,1,1,1,1,0,1,1,1,0
0,1,1,1,0,0,1,1,1,0
0,1,1,1,1,1,0,1,1,0
0,1,1,1,0,1,0,1,1,0
0,1,1,1,1,0,0,1,1,0
0,1,1,1,0,0,0,1,1,1
0,1,1,0,1,1,1,1,1,0
0,1,1,0,0,1,1,1,1,0
0,1,1,0,1,0,1,1,1,0
0,1,1,0,0,0,1,1,1,0
0,1,1,0,1,1,0,1,1,0
0,1,1,0,0,1,0,1,1,1
0,1,1,0,1,0,0,1,1,0
0,1,1,0,0,0,0,1,1,0
1,1,1,1,1,1,1,0,1,0
1,1,1,1,0,1,1,0,1,0
1,1,1,1,1,0,1,0,1,1
1,1,1,1,0,0,1,0,1,0
1,1,1,1,1,1,0,0,1,1
1,1,1,1,0,1,0,0,1,0
1,1,1,1,1,0,0,0,1,0
1,1,1,1,0,0,0,0,1,0
1,1,1,0,1,1,1,0,1,0
1,1,1,0,0,1,1,0,1,1
1,1,1,0,1,0,1,0,1,1
1,1,1,0,0,0,1,0,1,1
1,1,1,0,1,1,0,0,1,1
1,1,1,0,0,1,0,0,1,0
1,1,1,0,1,0,0,0,1,1
1,1,1,0,0,0,0,0,1,0
0,1,1,1,1,1,1,0,1,0
0,1,1,1,0,1,1,0,1,0
0,1,1,1,1,0,1,0,1,0
0,1,1,1,0,0,1,0,1,0
0,1,1,1,1,1,0,0,1,0
0,1,1,1,0,1,0,0,1,1
0,1,1,1,1,0,0,0,1,0
0,1,1,1,0,0,0,0,1,0
0,1,1,0,1,1,1,0,1,0
0,1,1,0,0,1,1,0,1,0
0,1,1,0,1,0,1,0,1,0
0,1,1,0,0,0,1,0,1,1
0,1,1,0,1,1,0,0,1,0
0,1,1,0,0,1,0,0,1,0
0,1,1,0,1,0,0,0,1,1
0,1,1,0,0,0,0,0,1,1
1,1,0,1,1,1,1,1,1,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,1,0,1,1,1,0
1,1,0,1,0,0,1,1,1,0
1,1,0,1,1,1,0,1,1,0
1,1,0,1,0,1,0,1,1,0
1,1,0,1,1,0,0,1,1,0
1,1,0,1,0,0,0,1,1,0
1,1,0,0,1,1,1,1,1,1
1,1,0,0,0,1,1,1,1,0
1,1,0,0,1,0,1,1,1,0
1,1,0,0,0,0,1,1,1,0
1,1,0,0,1,1,0,1,1,0
1,1,0,0,0,1,0,1,1,0
1,1,0,0,1,0,0,1,1,1
1,1,0,0,0,0,0,1,1,0
0,1,0,1,1,1,1,1,1,0
0,1,0,1,0,1,1,1,1,0
0,1,0,1,1,0,1,1,1,0
0,1,0,1,0,0,1,1,1,1
0,1,0,1,1,1,0,1,1,0
0,1,0,1,0,1,0,1,1,0
0,1,0,1,1,0,0,1,1,0
0,1,0,1,0,0,0,1,1,1
0,1,0,0,1,1,1,1,1,0
0,1,0,0,0,1,1,1,1,0
0,1,0,0,1,0,1,1,1,0
0,1,0,0,0,0,1,1,1,0
0,1,0,0,1,1,0,1,1,0
0,1,0,0,0,1,0,1,1,1
0,1,0,0,1,0,0,1,1,0
0,1,0,0,0,0,0,1,1,0
1,1,0,1,1,1,1,0,1,0
1,1,0,1,0,1,1,0,1,0
1,1,0,1,1,0,1,0,1,0
1,1,0,1,0,0,1,0,1,0
1,1,0,1,1,1,0,0,1,0
1,1,0,1,0,1,0,0,1,0
1,1,0,1,1,0,0,0,1,0
1,1,0,1,0,0,0,0,1,0
1,1,0,0,1,1,1,0,1,1
1,1,0,0,0,1,1,0,1,0
1,1,0,0,1,0,1,0,1,1
1,1,0,0,0,0,1,0,1,0
1,1,0,0,1,1,0,0,1,0
1,1,0,0,0,1,0,0,1,0
1,1,0,0,1,0,0,0,1,0
1,1,0,0,0,0,0,0,1,1
0,1,0,1,1,1,1,0,1,0
0,1,0,1,0,1,1,0,1,0
0,1,0,1,1,0,1,0,1,1
0,1,0,1,0,0,1,0,1,0
0,1,0,1,1,1,0,0,1,0
0,1,0,1,0,1,0,0,1,1
0,1,0,1,1,0,0,0,1,0
0,1,0,1,0,0,0,0,1,0
0,1,0,0,1,1,1,0,1,0
0,1,0,0,0,1,1,0,1,0
0,1,0,0,1,0,1,0,1,0
0,1,0,0,0,0,1,0,1,0
0,1,0,0,1,1,0,0,1,0
0,1,0,0,0,1,0,0,1,0
0,1,0,0,1,0,0,0,1,0
0,1,0,0,0,0,0,0,1,0
1,0,1,1,1,1,1,1,1,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,1,0,1,1,1,0
1,0,1,1,0,0,1,1,1,1
1,0,1,1,1,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
1,0,1,1,1,0,0,1,1,1
1,0,1,1,0,0,0,1,1,1
1,0,1,0,1,1,1,1,1,1
1,0,1,0,0,1,1,1,1,0
1,0,1,0,1,0,1,1,1,1
1,0,1,0,0,0,1,1,1,1
1,0,1,0,1,1,0,1,1,0
1,0,1,0,0,1,0,1,1,0
1,0,1,0,1,0,0,1,1,1
1,0,1,0,0,0,0,1,1,0
0,0,1,1,1,1,1,1,1,0
0,0,1,1,0,1,1,1,1,0
0,0,1,1,1,0,1,1,1,0
0,0,1,1,0,0,1,1,1,0
0,0,1,1,1,1,0,1,1,0
0,0,1,1,0,1,0,1,1,0
0,0,1,1,1,0,0,1,1,0
0,0,1,1,0,0,0,1,1,0
0,0,1,0,1,1,1,1,1,0
0,0,1,0,0,1,1,1,1,0
0,0,1,0,1,0,1,1,1,0
0,0,1,0,0,0,1,1,1,1
0,0,1,0,1,1,0,1,1,1
0,0,1,0,0,1,0,1,1,0
0,0,1,0,1,0,0,1,1,0
0,0,1,0,0,0,0,1,1,0
1,0,1,1,1,1,1,0,1,1
1,0,1,1,0,1,1,0,1,0
1,0,1,1,1,0,1,0,1,1
1,0,1,1,0,0,1,0,1,1
1,0,1,1,1,1,0,0,1,0
1,0,1,1,0,1,0,0,1,0
1,0,1,1,1,0,0,0,1,1
1,0,1,1,0,0,0,0,1,0
1,0,1,0,1,1,1,0,1,1
1,0,1,0,0,1,1,0,1,1
1,0,1,0,1,0,1,0,1,0
1,0,1,0,0,0,1,0,1,0
1,0,1,0,1,1,0,0,1,1
1,0,1,0,0,1,0,0,1,0
1,0,1,0,1,0,0,0,1,0
1,0,1,0,0,0,0,0,1,0
0,0,1,1,1,1,1,0,1,0
0,0,1,1,0,1,1,0,1,1
0,0,1,1,1,0,1,0,1,0
0,0,1,1,0,0,1,0,1,0
0,0,1,1,1,1,0,0,1,0
0,0,1,1,0,1,0,0,1,0
0,0,1,1,1,0,0,0,1,1
0,0,1,1,0,0,0,0,1,0
0,0,1,0,1,1,1,0,1,0
0,0,1,0,0,1,1,0,1,0
0,0,1,0,1,0,1,0,1,0
0,0,1,0,0,0,1,0,1,1
0,0,1,0,1,1,0,0,1,0
0,0,1,0,0,1,0,0,1,0
0,0,1,0,1,0,0,0,1,1
0,0,1,0,0,0,0,0,1,1
1,0,0,1,1,1,1,1,1,1
1,0,0,1,0,1,1,1,1,0
1,0,0,1,1,0,1,1,1,1
1,0,0,1,0,0,1,1,1,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,0,1,0,1,1,0
1,0,0,1,1,0,0,1,1,0
1,0,0,1,0,0,0,1,1,0
1,0,0,0,1,1,1,1,1,0
1,0,0,0,0,1,1,1,1,0
1,0,0,0,1,0,1,1,1,1
1,0,0,0,0,0,1,1,1,0
1,0,0,0,1,1,0,1,1,0
1,0,0,0,0,1,0,1,1,0
1,0,0,0,1,0,0,1,1,0
1,0,0,0,0,0,0,1,1,1
0,0,0,1,1,1,1,1,1,0
0,0,0,1,0,1,1,1,1,1
0,0,0,1,1,0,1,1,1,0
0,0,0,1,0,0,1,1,1,0
0,0,0,1,1,1,0,1,1,0
0,0,0,1,0,1,0,1,1,1
0,0,0,1,1,0,0,1,1,0
0,0,0,1,0,0,0,1,1,0
0,0,0,0,1,1,1,1,1,0
0,0,0,0,0,1,1,1,1,0
0,0,0,0,1,0,1,1,1,1
0,0,0,0,0,0,1,1,1,0
0,0,0,0,1,1,0,1,1,0
0,0,0,0,0,1,0,1,1,0
0,0,0,0,1,0,0,1,1,0
0,0,0,0,0,0,0,1,1,0
1,0,0,1,1,1,1,0,1,0
1,0,0,1,0,1,1,0,1,0
1,0,0,1,1,0,1,0,1,1
1,0,0,1,0,0,1,0,1,0
1,0,0,1,1,1,0,0,1,1
1,0,0,1,0,1,0,0,1,0
1,0,0,1,1,0,0,0,1,0
1,0,0,1,0,0,0,0,1,0
1,0,0,0,1,1,1,0,1,1
1,0,0,0,0,1,1,0,1,0
1,0,0,0,1,0,1,0,1,0
1,0,0,0,0,0,1,0,1,0
1,0,0,0,1,1,0,0,1,0
1,0,0,0,0,1,0,0,1,0
1,0,0,0,1,0,0,0,1,1
1,0,0,0,0,0,0,0,1,1
0,0,0,1,1,1,1,0,1,0
0,0,0,1,0,1,1,0,1,0
0,0,0,1,1,0,1,0,1,0
0,0,0,1,0,0,1,0,1,0
0,0,0,1,1,1,0,0,1,0
0,0,0,1,0,1,0,0,1,0
0,0,0,1,1,0,0,0,1,0
0,0,0,1,0,0,0,0,1,0
0,0,0,0,1,1,1,0,1,1
0,0,0,0,0,1,1,0,1,0
0,0,0,0,1,0,1,0,1,1
0,0,0,0,0,0,1,0,1,1
0,0,0,0,1,1,0,0,1,0
0,0,0,0,0,1,0,0,1,0
0,0,0,0,1,0,0,0,1,0
0,0,0,0,0,0,0,0,1,0
1,1,1,1,1,1,1,1,0,0
1,1,1,1,0,1,1,1,0,0
1,1,1,1,1,0,1,1,0,0
1,1,1,1,0,0,1,1,0,0
1,1,1,1,1,1,0,1,0,0
1,1,1,1,0,1,0,1,0,0
1,1,1,1,1,0,0,1,0,0
1,1,1,1,0,0,0,1,0,0
1,1,1,0,1,1,1,1,0,0
1,1,1,0,0,1,1,1,0,0
1,1,1,0,1,0,1,1,0,0
1,1,1,0,0,0,1,1,0,0
1,1,1,0,1,1,0,1,0,0
1,1,1,0,0,1,0,1,0,0
1,1,1,0,1,0,0,1,0,0
1,1,1,0,0,0,0,1,0,0
0,1,1,1,1,1,1,1,0,0
0,1,1,1,0,1,1,1,0,0
0,1,1,1,1,0,1,1,0,0
0,1,1,1,0,0,1,1,0,0
0,1,1,1,1,1,0,1,0,0
0,1,1,1,0,1,0,1,0,0
0,1,1,1,1,0,0,1,0,1
0,1,1,1,0,0,0,1,0,1
0,1,1,0,1,1,1,1,0,0
0,1,1,0,0,1,1,1,0,0
0,1,1,0,1,0,1,1,0,1
0,1,1,0,0,0,1,1,0,0
0,1,1,0,1,1,0,1,0,0
0,1,1,0,0,1,0,1,0,1
0,1,1,0,1,0,0,1,0,0
0,1,1,0,0,0,0,1,0,0
1,1,1,1,1,1,1,0,0,1
1,1,1,1,0,1,1,0,0,0
1,1,1,1,1,0,1,0,0,0
1,1,1,1,0,0,1,0,0,1
1,1,1,1,1,1,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,0,0,0,0,0
1,1,1,0,1,1,1,0,0,1
1,1,1,0,0,1,1,0,0,0
1,1,1,0,1,0,1,0,0,1
1,1,1,0,0,0,1,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,0,1,0,0,0,0
1,1,1,0,1,0,0,0,0,0
1,1,1,0,0,0,0,0,0,1
0,1,1,1,1,1,1,0,0,0
0,1,1,1,0,1,1,0,0,0
0,1,1,1,1,0,1,0,0,0
0,1,1,1,0,0,1,0,0,0
0,1,1,1,1,1,0,0,0,1
0,1,1,1,0,1,0,0,0,1
0,1,1,1,1,0,0,0,0,0
0,1,1,1,0,0,0,0,0,0
0,1,1,0,1,1,1,0,0,0
0,1,1,0,0,1,1,0,0,0
0,1,1,0,1,0,1,0,0,0
0,1,1,0,0,0,1,0,0,0
0,1,1,0,1,1,0,0,0,0
0,1,1,0,0,1,0,0,0,0
0,1,1,0,1,0,0,0,0,0
0,1,1,0,0,0,0,0,0,0
1,1,0,1,1,1,1,1,0,0
1,1,0,1,0,1,1,1,0,0
1,1,0,1,1,0,1,1,0,0
1,1,0,1,0,0,1,1,0,0
1,1,0,1,1,1,0,1,0,0
1,1,0,1,0,1,0,1,0,0
1,1,0,1,1,0,0,1,0,0
1,1,0,1,0,0,0,1,0,0
1,1,0,0,1,1,1,1,0,0
1,1,0,0,0,1,1,1,0,0
1,1,0,0,1,0,1,1,0,0
1,1,0,0,0,0,1,1,0,0
1,1,0,0,1,1,0,1,0,0
1,1,0,0,0,1,0,1,0,0
1,1,0,0,1,0,0,1,0,0
1,1,0,0,0,0,0,1,0,1
0,1,0,1,1,1,1,1,0,0
0,1,0,1,0,1,1,1,0,0
0,1,0,1,1,0,1,1,0,0
0,1,0,1,0,0,1,1,0,1
0,1,0,1,1,1,0,1,0,0
0,1,0,1,0,1,0,1,0,0
0,1,0,1,1,0,0,1,0,1
0,1,0,1,0,0,0,1,0,0
0,1,0,0,1,1,1,1,0,1
0,1,0,0,0,1,1,1,0,1
0,1,0,0,1,0,1,1,0,0
0,1,0,0,0,0,1,1,0,0
0,1,0,0,1,1,0,1,0,1
0,1,0,0,0,1,0,1,0,0
0,1,0,0,1,0,0,1,0,0
0,1,0,0,0,0,0,1,0,1
1,1,0,1,1,1,1,0,0,0
1,1,0,1,0,1,1,0,0,0
1,1,0,1,1,0,1,0,0,0
1,1,0,1,0,0,1,0,0,0
1,1,0,1,1,1,0,0,0,0
1,1,0,1,0,1,0,0,0,0
1,1,0,1,1,0,0,0,0,0
1,1,0,1,0,0,0,0,0,1
1,1,0,0,1,1,1,0,0,0
1,1,0,0,0,1,1,0,0,0
1,1,0,0,1,0,1,0,0,0
1,1,0,0,0,0,1,0,0,0
1,1,0,0,1,1,0,0,0,0
1,1,0,0,0,1,0,0,0,0
1,1,0,0,1,0,0,0,0,0
1,1,0,0,0,0,0,0,0,1
0,1,0,1,1,1,1,0,0,1
0,1,0,1,0,1,1,0,0,1
0,1,0,1,1,0,1,0,0,0
0,1,0,1,0,0,1,0,0,0
0,1,0,1,1,1,0,0,0,1
0,1,0,1,0,1,0,0,0,0
0,1,0,1,1,0,0,0,0,0
0,1,0,1,0,0,0,0,0,1
0,1,0,0,1,1,1,0,0,0
0,1,0,0,0,1,1,0,0,0
0,1,0,0,1,0,1,0,0,0
0,1,0,0,0,0,1,0,0,0
0,1,0,0,1,1,0,0,0,0
0,1,0,0,0,1,0,0,0,1
0,1,0,0,1,0,0,0,0,0
0,1,0,0,0,0,0,0,0,0
1,0,1,1,1,1,1,1,0,1
1,0,1,1,0,1,1,1,0,0
1,0,1,1,1,0,1,1,0,1
1,0,1,1,0,0,1,1,0,0
1,0,1,1,1,1,0,1,0,0
1,0,1,1,0,1,0,1,0,0
1,0,1,1,1,0,0,1,0,0
1,0,1,1,0,0,0,1,0,0
1,0,1,0,1,1,1,1,0,0
1,0,1,0,0,1,1,1,0,1
1,0,1,0,1,0,1,1,0,1
1,0,1,0,0,0,1,1,0,0
1,0,1,0,1,1,0,1,0,0
1,0,1,0,0,1,0,1,0,0
1,0,1,0,1,0,0,1,0,0
1,0,1,0,0,0,0,1,0,0
0,0,1,1,1,1,1,1,0,0
0,0,1,1,0,1,1,1,0,0
0,0,1,1,1,0,1,1,0,0
0,0,1,1,0,0,1,1,0,0
0,0,1,1,1,1,0,1,0,1
0,0,1,1,0,1,0,1,0,1
0,0,1,1,1,0,0,1,0,0
0,0,1,1,0,0,0,1,0,0
0,0,1,0,1,1,1,1,0,0
0,0,1,0,0,1,1,1,0,0
0,0,1,0,1,0,1,1,0,0
0,0,1,0,0,0,1,1,0,0
0,0,1,0,1,1,0,1,0,0
0,0,1,0,0,1,0,1,0,0
0,0,1,0,1,0,0,1,0,0
0,0,1,0,0,0,0,1,0,0
1,0,1,1,1,1,1,0,0,0
1,0,1,1,0,1,1,0,0,0
1,0,1,1,1,0,1,0,0,1
1,0,1,1,0,0,1,0,0,0
1,0,1,1,1,1,0,0,0,0
1,0,1,1,0,1,0,0,0,0
1,0,1,1,1,0,0,0,0,0
1,0,1,1,0,0,0,0,0,1
1,0,1,0,1,1,1,0,0,1
1,0,1,0,0,1,1,0,0,0
1,0,1,0,1,0,1,0,0,0
1,0,1,0,0,0,1,0,0,1
1,0,1,0,1,1,0,0,0,0
1,0,1,0,0,1,0,0,0,0
1,0,1,0,1,0,0,0,0,0
1,0,1,0,0,0,0,0,0,1
0,0,1,1,1,1,1,0,0,0
0,0,1,1,0,1,1,0,0,0
0,0,1,1,1,0,1,0,0,1
0,0,1,1,0,0,1,0,0,0
0,0,1,1,1,1,0,0,0,0
0,0,1,1,0,1,0,0,0,0
0,0,1,1,1,0,0,0,0,0
0,0,1,1,0,0,0,0,0,0
0,0,1,0,1,1,1,0,0,1
0,0,1,0,0,1,1,0,0,0
0,0,1,0,1,0,1,0,0,1
0,0,1,0,0,0,1,0,0,0
0,0,1,0,1,1,0,0,0,0
0,0,1,0,0,1,0,0,0,0
0,0,1,0,1,0,0,0,0,1
0,0,1,0,0,0,0,0,0,0
1,0,0,1,1,1,1,1,0,0
1,0,0,1,0,1,1,1,0,0
1,0,0,1,1,0,1,1,0,1
1,0,0,1,0,0,1,1,0,0
1,0,0,1,1,1,0,1,0,0
1,0,0,1,0,1,0,1,0,0
1,0,0,1,1,0,0,1,0,0
1,0,0,1,0,0,0,1,0,0
1,0,0,0,1,1,1,1,0,0
1,0,0,0,0,1,1,1,0,0
1,0,0,0,1,0,1,1,0,0
1,0,0,0,0,0,1,1,0,1
1,0,0,0,1,1,0,1,0,0
1,0,0,0,0,1,0,1,0,1
1,0,0,0,1,0,0,1,0,0
1,0,0,0,0,0,0,1,0,1
0,0,0,1,1,1,1,1,0,1
0,0,0,1,0,1,1,1,0,1
0,0,0,1,1,0,1,1,0,0
0,0,0,1,0,0,1,1,0,0
0,0,0,1,1,1,0,1,0,1
0,0,0,1,0,1,0,1,0,0
0,0,0,1,1,0,0,1,0,0
0,0,0,1,0,0,0,1,0,1
0,0,0,0,1,1,1,1,0,0
0,0,0,0,0,1,1,1,0,0
0,0,0,0,1,0,1,1,0,0
0,0,0,0,0,0,1,1,0,0
0,0,0,0,1,1,0,1,0,0
0,0,0,0,0,1,0,1,0,1
0,0,0,0,1,0,0,1,0,0
0,0,0,0,0,0,0,1,0,0
1,0,0,1,1,1,1,0,0,0
1,0,0,1,0,1,1,0,0,0
1,0,0,1,1,0,1,0,0,0
1,0,0,1,0,0,1,0,0,0
1,0,0,1,1,1,0,0,0,0
1,0,0,1,0,1,0,0,0,1
1,0,0,1,1,0,0,0,0,1
1,0,0,1,0,0,0,0,0,1
1,0,0,0,1,1,1,0,0,0
1,0,0,0,0,1,1,0,0,1
1,0,0,0,1,0,1,0,0,0
1,0,0,0,0,0,1,0,0,1
1,0,0,0,1,1,0,0,0,1
1,0,0,0,0,1,0,0,0,1
1,0,0,0,1,0,0,0,0,1
1,0,0,0,0,0,0,0,0,0
0,0,0,1,1,1,1,0,0,0
0,0,0,1,0,1,1,0,0,0
0,0,0,1,1,0,1,0,0,0
0,0,0,1,0,0,1,0,0,0
0,0,0,1,1,1,0,0,0,0
0,0,0,1,0,1,0,0,0,1
0,0,0,1,1,0,0,0,0,0
0,0,0,1,0,0,0,0,0,0
0,0,0,0,1,1,1,0,0,1
0,0,0,0,0,1,1,0,0,0
0,0,0,0,1,0,1,0,0,1
0,0,0,0,0,0,1,0,0,0
0,0,0,0,1,1,0,0,0,0
0,0,0,0,0,1,0,0,0,0
0,0,0,0,1,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0

[M. I. Wright]

Oh, awesome! Glider guns GGa and GGb in RLE format:

Code: Select all

x = 57, y = 7, rule = x-rule
2o24b2o2b2o23b2o$bo24bo4bo23bo$6b2o12b2o15bo8bo2bo$5bo16bo13bo13bo$6b
2o12b2o15bo8bo2bo$bo24bo4bo23bo$2o24b2o2b2o23b2o!

[Saka]

Code: Select all

x = 4, y = 4, rule = x-rule
o$o$bo$2b2o!

Code: Select all

x = 9, y = 9, rule = x-rule
bo$obo$obo4$6b2o$8bo$6b2o!

shifter

Code: Select all

x = 3, y = 6, rule = x-rule
b2o3$2bo$bo$bo!

[danieldb]

p2:

Code: Select all

x = 5, y = 5, rule = x-rule
bobo$o3bo2$o3bo$bobo!

Splitters(?):

Code: Select all

x = 55, y = 8, rule = x-rule
o7bo37bo7bo$o7bo37bo7bo4$50bo$4bo44bobo$3bobo!

Oscillators that follow an unknown (as of now) formula:

Code: Select all

x = 5, y = 7, rule = x-rule
o3bo$o3bo$2bo$bobo2$o3bo$o3bo!

Code: Select all

x = 18, y = 40, rule = x-rule
2o4b2o$3bo$2bo$3bo$2o4b2o3$2o6b2o$3bo$2bo$3bo$2o6b2o3$2o8b2o$3bo$2bo$
3bo$2o8b2o3$2o10b2o$3bo$2bo$3bo$2o10b2o3$2o12b2o$3bo$2bo$3bo$2o12b2o3$
2o14b2o$3bo$2bo$3bo$2o14b2o!

Sequence is 2, 8, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126, 134, 142, ...

Glider eater:

Code: Select all

x = 3, y = 5, rule = x-rule
2bo$2bo$o$bo$bo!

[M. I. Wright]

Code: Select all

x = 4, y = 4, rule = x-rule
o$o$bo$2b2o!

This was mentioned in the paper.

@danieldb Neat! Most soups just devolve into still-lifes and spaceships, so I was starting to think that the rule didn't have any oscillators.

By the way, I kinda doubt that guns are impossible in the isotropic X-rule predecessor... I'll make a ruletable for it soon to search around for one.

[danieldb]

orthogonal glider to diagonal glider and *almost* diag to ortho:

Code: Select all

x = 12, y = 11, rule = x-rule
7bobo$8bo$o$o7$10b2o!

[danieldb]

selfdestruct reflectors:

Code: Select all

x = 7, y = 328, rule = x-rule
bo3bo$bo3bo$3bo$2bobo3$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5b
o$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o
5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo
9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o
5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$
o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo!

[jmgomez]

Hello!

I’m sorry that I’m late, I was so busy so until today I see the forum.
I’m glad that you find the relation between mapping and neighborhood!

Yes!


The X-rule mapping

y4voCZm.png (24.42 KiB) Viewed 625 times

correspond to the next neighborhoods:

5G6hz5e.png (160.31 KiB) Viewed 625 times

Best Regards
-José Manuel Gómez Soto

[praosylen]

A rake:

Code: Select all

x = 16, y = 27, rule = x-rule
7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo$8bo4bo$10b2o3$10b2o$9bo2bo$2bo
7b2o$bobo3b2o4b2o$5bob3o2b3o$o3b3obo4bobo$5bobo6bo$2bo7b2o2$8bo$8bo$6b
2ob2o$8bo$8bo3$9bo2$8b2o!

Another:

Code: Select all

x = 8, y = 9, rule = x-rule
bobo$o$bobo2$3bo$bo$o$bo5bo$3bo!

And another:

Code: Select all

x = 13, y = 4, rule = x-rule
bo4bo4bo$obo2bobo2bobo2$10bobo!

[danieldb]

A sideways only glider:

Code: Select all

x = 4, y = 4, rule = x-rule
3bo$bo$o$bobo!

And 3 tagalongs:

Code: Select all

x = 18, y = 11, rule = x-rule
15bo$15bo$13bo3bo2$7b3o4b3o$bo$bo2$bo6bo6bo$obo4bobo4bobo$obo4bobo4bob
o!

This is certainly an amazing rule

[jmgomez]

Hello,

X-Rule have oscillators, actually one of the is the name of rule "X".

Try with this

DOcHzEu.png (1.14 KiB) Viewed 625 times

And of course if you put the reflector in large distances you will obtain oscillators of different periodic behavior.

Sorry I do not send Golly format.
Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

Best Regards
-jm

PD: Nice oscillator Aidan F. Pierce!

[danieldb]

A rake:

Code: Select all

x = 16, y = 27, rule = x-rule
7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo$8bo4bo$10b2o3$10b2o$9bo2bo$2bo
7b2o$bobo3b2o4b2o$5bob3o2b3o$o3b3obo4bobo$5bobo6bo$2bo7b2o2$8bo$8bo$6b
2ob2o$8bo$8bo3$9bo2$8b2o!

Another:

Code: Select all

x = 8, y = 9, rule = x-rule
bobo$o$bobo2$3bo$bo$o$bo5bo$3bo!

And another:

Code: Select all

x = 13, y = 4, rule = x-rule
bo4bo4bo$obo2bobo2bobo2$10bobo!

Cool we can now create spaceships and puffers:

Ship called "Collider":

Code: Select all

x = 34, y = 27, rule = x-rule
7bobo2bobo4bobo2bobo$7bobo2bobo4bobo2bobo$6b2ob4ob2o2b2ob4ob2o$8bo4bo
6bo4bo$8bo4bo6bo4bo$10b2o10b2o3$10b2o10b2o$9bo2bo8bo2bo$2bo7b2o10b2o7b
o$bobo3b2o4b2o4b2o4b2o3bobo$5bob3o2b3o4b3o2b3obo$o3b3obo4bobo2bobo4bob
3o3bo$5bobo6bo4bo6bobo$2bo7b2o10b2o7bo2$8bo16bo$8bo16bo$6b2ob2o12b2ob
2o$8bo16bo$8bo16bo3$9bo14bo2$8b2o14b2o!

Domino Puffer:

Code: Select all

x = 35, y = 30, rule = x-rule
7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo6bobo2bobo$8bo4bo6bobo2bobo$10b
2o7b2ob4ob2o$21bo4bo$21bo4bo$10b2o11b2o$9bo2bo$2bo7b2o$bobo3b2o4b2o8b
2o$5bob3o2b3o7bo2bo$o3b3obo4bobo7b2o7bo$5bobo6bo5b2o4b2o3bobo$2bo7b2o
8b3o2b3obo$19bobo4bob3o3bo$8bo11bo6bobo$8bo14b2o7bo$6b2ob2o$8bo17bo$8b
o17bo$24b2ob2o$26bo$9bo16bo2$8b2o$25bo2$25b2o!

Pre-Block Puffer:

Code: Select all

x = 52, y = 38, rule = x-rule
37bobo2bobo$37bobo2bobo$36b2ob4ob2o$38bo4bo$38bo4bo$40b2o3$40b2o$39bo
2bo$7bobo2bobo25b2o7bo$7bobo2bobo10bobo2bobo4b2o4b2o3bobo$6b2ob4ob2o9b
obo2bobo4b3o2b3obo$8bo4bo10b2ob4ob2o2bobo4bob3o3bo$8bo4bo12bo4bo5bo6bo
bo$10b2o14bo4bo8b2o7bo$28b2o$43bo$10b2o31bo$9bo2bo15b2o11b2ob2o$2bo7b
2o15bo2bo12bo$bobo3b2o4b2o5bo7b2o13bo$5bob3o2b3o4bobo3b2o4b2o$o3b3obo
4bobo7bob3o2b3o$5bobo6bo3bo3b3obo4bobo8bo$2bo7b2o11bobo6bo$20bo7b2o12b
2o$8bo$8bo17bo$6b2ob2o15bo$8bo15b2ob2o$8bo17bo$26bo2$9bo$27bo$8b2o$26b
2o!

Forward Rake:

Code: Select all

x = 52, y = 40, rule = x-rule
37bobo2bobo$37bobo2bobo$19bobo2bobo9b2ob4ob2o$19bobo2bobo11bo4bo$18b2o
b4ob2o10bo4bo$20bo4bo14b2o$20bo4bo$22b2o$40b2o$39bo2bo$22b2o16b2o7bo$
21bo2bo12b2o4b2o3bobo$22b2o7bo5b3o2b3obo$7bobo2bobo4b2o4b2o3bobo3bobo
4bob3o3bo$7bobo2bobo4b3o2b3obo8bo6bobo$6b2ob4ob2o2bobo4bob3o3bo6b2o7bo
$8bo4bo5bo6bobo$8bo4bo8b2o7bo11bo$10b2o31bo$25bo15b2ob2o$25bo17bo$10b
2o11b2ob2o15bo$9bo2bo12bo$2bo7b2o13bo$bobo3b2o4b2o27bo$5bob3o2b3o$o3b
3obo4bobo8bo17b2o$5bobo6bo$2bo7b2o12b2o2$8bo$8bo$6b2ob2o$8bo$8bo3$9bo
2$8b2o!

[danieldb]

Hello,

X-Rule have oscillators, actually one of the is the name of rule "X".

Try with this



And of course if you put the reflector in large distances you will obtain oscillators of different periodic behavior.

Sorry I do not send Golly format.
Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

Best Regards
-jm

PD: Nice oscillator Aidan F. Pierce!

Check my other posts for a simplification of this

[thunk]

Oscillators that follow an unknown (as of now) formula:

From the third and onward, it's just a horizontal glider between two 180 deg reflectors. Every 2 ticks increases period by 8.

The complete periods p are shown below. For increasing even gaps g, period p increases by +8 time-steps.

@danieldb Neat! Most soups just devolve into still-lifes and spaceships, so I was starting to think that the rule didn't have any oscillators.

Pseudoclock is also a p2 oscillator:

Code: Select all

x = 4, y = 4, rule = x-rule
2bo$2o$2b2o$bo!

EDIT: added reference.

[jmgomez]

Nice!!

-jm

[Billabob]

Another P2:

Code: Select all

x = 6, y = 8, rule = x-rule
4b2o$5bo$3bo$3b2o$b2o$2bo$o$2o!

[thunk]

Sorry I do not send Golly format.
Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

You can select dvgrn's rule table and copy, then paste, it into the Golly window (M. I. Wright's tables, as stated, are not the X-Rule). It should then say "created (directory)\x-rule". Then you can just draw in the open window, or paste other patterns in the same way.

[jmgomez]

Thanks for you explain to me.

I get it!!

Thank you so much!!!



-jm

[M. I. Wright]

Oops, I forgot about the oscillators mentioned in the paper

jm: Great! Golly's pattern format is just run-length encoding; 'o' stands for an ON cell, 'b' is for an OFF cell, and '$' is a newline. So this:

Code: Select all

2bo2$o3bo2$bobo$2bo!

is the same as this ('.' is for OFF and * is for ON):

Code: Select all

..*..
.....
*...*
.....
.*.*.
..*..

The rule-table format is pretty straightforward as well. First comes the header:

Code: Select all

@RULE <rulename>

comments can go here, or included below if preceded by a #

@TABLE
n_states:2            #number of cell states. X-rule only has two (on and off), but Golly supports up to 256
neighborhood:Moore    #self-explanatory. Other neighborhoods include vonNeumann and hexagonal

After that is the transitions. This is the format for a Moore neighborhood:

Code: Select all

s,1,2,3,4,5,6,7,8,f

where 's' stands for 'starting cell state' and 'f' means 'final'. The numbers follow this configuration:

Code: Select all

8 1 2
7 s 3
6 5 4

For instance, the transition

Code: Select all

0,1,1,1,0,1,1,0,0,1

means that in

Code: Select all

1 1 1
0 0 1
1 1 0

the middle cell (0) will become 1.

Hope this clears things up! You can look in Golly's Help menu for more details.

[jmgomez]

M. I. Wright:

Best Regards
-jm

[jmgomez]

Hello eveybody,

Andrew Wuensche and me, just explore the minimun patterns (and few more) in order to show logical universal computation in X-Rule, so they are many possibilities to explore!

You are so welcome!

Best Regards
-jm