## X-Rule

For discussion of other cellular automata.

### X-Rule

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
jmgomez

Posts: 43
Joined: October 6th, 2015, 1:42 am

### Re: X-Rule

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.)

@RULE not-x-rule@TABLETo open this rule, hit 'select all', copy it, then paste into Gollyn_states:2neighborhood:Mooresymmetries:none# The first digit represents the current cell, the next eight its Moore neighborhood, and the final digit determines that configuration's output1,1,1,1,1,1,1,1,1,01,1,1,1,1,1,1,1,0,01,1,1,1,1,1,1,0,1,01,1,1,1,1,1,1,0,0,11,1,1,1,1,1,0,1,1,01,1,1,1,1,1,0,1,0,01,1,1,1,1,1,0,0,1,11,1,1,1,1,1,0,0,0,01,1,1,1,1,0,1,1,1,01,1,1,1,1,0,1,1,0,11,1,1,1,1,0,1,0,1,11,1,1,1,1,0,1,0,0,01,1,1,1,1,0,0,1,1,01,1,1,1,1,0,0,1,0,01,1,1,1,1,0,0,0,1,01,1,1,1,1,0,0,0,0,01,1,1,1,0,1,1,1,1,01,1,1,1,0,1,1,1,0,01,1,1,1,0,1,1,0,1,01,1,1,1,0,1,1,0,0,01,1,1,1,0,1,0,1,1,01,1,1,1,0,1,0,1,0,01,1,1,1,0,1,0,0,1,01,1,1,1,0,1,0,0,0,11,1,1,1,0,0,1,1,1,01,1,1,1,0,0,1,1,0,01,1,1,1,0,0,1,0,1,01,1,1,1,0,0,1,0,0,01,1,1,1,0,0,0,1,1,01,1,1,1,0,0,0,1,0,11,1,1,1,0,0,0,0,1,01,1,1,1,0,0,0,0,0,01,1,1,0,1,1,1,1,1,01,1,1,0,1,1,1,1,0,01,1,1,0,1,1,1,0,1,11,1,1,0,1,1,1,0,0,01,1,1,0,1,1,0,1,1,11,1,1,0,1,1,0,1,0,01,1,1,0,1,1,0,0,1,01,1,1,0,1,1,0,0,0,01,1,1,0,1,0,1,1,1,01,1,1,0,1,0,1,1,0,11,1,1,0,1,0,1,0,1,11,1,1,0,1,0,1,0,0,11,1,1,0,1,0,0,1,1,11,1,1,0,1,0,0,1,0,01,1,1,0,1,0,0,0,1,11,1,1,0,1,0,0,0,0,01,1,1,0,0,1,1,1,1,01,1,1,0,0,1,1,1,0,01,1,1,0,0,1,1,0,1,01,1,1,0,0,1,1,0,0,01,1,1,0,0,1,0,1,1,01,1,1,0,0,1,0,1,0,11,1,1,0,0,1,0,0,1,01,1,1,0,0,1,0,0,0,01,1,1,0,0,0,1,1,1,01,1,1,0,0,0,1,1,0,01,1,1,0,0,0,1,0,1,01,1,1,0,0,0,1,0,0,11,1,1,0,0,0,0,1,1,01,1,1,0,0,0,0,1,0,01,1,1,0,0,0,0,0,1,11,1,1,0,0,0,0,0,0,11,1,0,1,1,1,1,1,1,01,1,0,1,1,1,1,1,0,01,1,0,1,1,1,1,0,1,01,1,0,1,1,1,1,0,0,01,1,0,1,1,1,0,1,1,01,1,0,1,1,1,0,1,0,01,1,0,1,1,1,0,0,1,01,1,0,1,1,1,0,0,0,01,1,0,1,1,0,1,1,1,11,1,0,1,1,0,1,1,0,01,1,0,1,1,0,1,0,1,01,1,0,1,1,0,1,0,0,01,1,0,1,1,0,0,1,1,01,1,0,1,1,0,0,1,0,01,1,0,1,1,0,0,0,1,11,1,0,1,1,0,0,0,0,01,1,0,1,0,1,1,1,1,01,1,0,1,0,1,1,1,0,01,1,0,1,0,1,1,0,1,01,1,0,1,0,1,1,0,0,11,1,0,1,0,1,0,1,1,01,1,0,1,0,1,0,1,0,01,1,0,1,0,1,0,0,1,01,1,0,1,0,1,0,0,0,11,1,0,1,0,0,1,1,1,01,1,0,1,0,0,1,1,0,01,1,0,1,0,0,1,0,1,01,1,0,1,0,0,1,0,0,01,1,0,1,0,0,0,1,1,01,1,0,1,0,0,0,1,0,11,1,0,1,0,0,0,0,1,01,1,0,1,0,0,0,0,0,01,1,0,0,1,1,1,1,1,01,1,0,0,1,1,1,1,0,01,1,0,0,1,1,1,0,1,01,1,0,0,1,1,1,0,0,01,1,0,0,1,1,0,1,1,01,1,0,0,1,1,0,1,0,01,1,0,0,1,1,0,0,1,01,1,0,0,1,1,0,0,0,01,1,0,0,1,0,1,1,1,11,1,0,0,1,0,1,1,0,01,1,0,0,1,0,1,0,1,11,1,0,0,1,0,1,0,0,01,1,0,0,1,0,0,1,1,01,1,0,0,1,0,0,1,0,01,1,0,0,1,0,0,0,1,01,1,0,0,1,0,0,0,0,11,1,0,0,0,1,1,1,1,01,1,0,0,0,1,1,1,0,01,1,0,0,0,1,1,0,1,11,1,0,0,0,1,1,0,0,01,1,0,0,0,1,0,1,1,01,1,0,0,0,1,0,1,0,11,1,0,0,0,1,0,0,1,01,1,0,0,0,1,0,0,0,01,1,0,0,0,0,1,1,1,01,1,0,0,0,0,1,1,0,01,1,0,0,0,0,1,0,1,01,1,0,0,0,0,1,0,0,01,1,0,0,0,0,0,1,1,01,1,0,0,0,0,0,1,0,01,1,0,0,0,0,0,0,1,01,1,0,0,0,0,0,0,0,01,0,1,1,1,1,1,1,1,01,0,1,1,1,1,1,1,0,01,0,1,1,1,1,1,0,1,01,0,1,1,1,1,1,0,0,11,0,1,1,1,1,0,1,1,01,0,1,1,1,1,0,1,0,01,0,1,1,1,1,0,0,1,11,0,1,1,1,1,0,0,0,11,0,1,1,1,0,1,1,1,11,0,1,1,1,0,1,1,0,01,0,1,1,1,0,1,0,1,11,0,1,1,1,0,1,0,0,11,0,1,1,1,0,0,1,1,01,0,1,1,1,0,0,1,0,01,0,1,1,1,0,0,0,1,11,0,1,1,1,0,0,0,0,01,0,1,1,0,1,1,1,1,01,0,1,1,0,1,1,1,0,01,0,1,1,0,1,1,0,1,01,0,1,1,0,1,1,0,0,01,0,1,1,0,1,0,1,1,01,0,1,1,0,1,0,1,0,01,0,1,1,0,1,0,0,1,01,0,1,1,0,1,0,0,0,01,0,1,1,0,0,1,1,1,01,0,1,1,0,0,1,1,0,01,0,1,1,0,0,1,0,1,01,0,1,1,0,0,1,0,0,11,0,1,1,0,0,0,1,1,11,0,1,1,0,0,0,1,0,01,0,1,1,0,0,0,0,1,01,0,1,1,0,0,0,0,0,01,0,1,0,1,1,1,1,1,11,0,1,0,1,1,1,1,0,01,0,1,0,1,1,1,0,1,11,0,1,0,1,1,1,0,0,11,0,1,0,1,1,0,1,1,01,0,1,0,1,1,0,1,0,01,0,1,0,1,1,0,0,1,11,0,1,0,1,1,0,0,0,01,0,1,0,1,0,1,1,1,11,0,1,0,1,0,1,1,0,11,0,1,0,1,0,1,0,1,01,0,1,0,1,0,1,0,0,01,0,1,0,1,0,0,1,1,11,0,1,0,1,0,0,1,0,01,0,1,0,1,0,0,0,1,01,0,1,0,1,0,0,0,0,01,0,1,0,0,1,1,1,1,01,0,1,0,0,1,1,1,0,11,0,1,0,0,1,1,0,1,01,0,1,0,0,1,1,0,0,01,0,1,0,0,1,0,1,1,01,0,1,0,0,1,0,1,0,01,0,1,0,0,1,0,0,1,11,0,1,0,0,1,0,0,0,01,0,1,0,0,0,1,1,1,01,0,1,0,0,0,1,1,0,01,0,1,0,0,0,1,0,1,01,0,1,0,0,0,1,0,0,11,0,1,0,0,0,0,1,1,01,0,1,0,0,0,0,1,0,01,0,1,0,0,0,0,0,1,11,0,1,0,0,0,0,0,0,11,0,0,1,1,1,1,1,1,11,0,0,1,1,1,1,1,0,01,0,0,1,1,1,1,0,1,11,0,0,1,1,1,1,0,0,01,0,0,1,1,1,0,1,1,01,0,0,1,1,1,0,1,0,01,0,0,1,1,1,0,0,1,01,0,0,1,1,1,0,0,0,01,0,0,1,1,0,1,1,1,01,0,0,1,1,0,1,1,0,01,0,0,1,1,0,1,0,1,11,0,0,1,1,0,1,0,0,01,0,0,1,1,0,0,1,1,01,0,0,1,1,0,0,1,0,01,0,0,1,1,0,0,0,1,01,0,0,1,1,0,0,0,0,11,0,0,1,0,1,1,1,1,01,0,0,1,0,1,1,1,0,11,0,0,1,0,1,1,0,1,01,0,0,1,0,1,1,0,0,01,0,0,1,0,1,0,1,1,01,0,0,1,0,1,0,1,0,11,0,0,1,0,1,0,0,1,01,0,0,1,0,1,0,0,0,01,0,0,1,0,0,1,1,1,01,0,0,1,0,0,1,1,0,01,0,0,1,0,0,1,0,1,11,0,0,1,0,0,1,0,0,01,0,0,1,0,0,0,1,1,01,0,0,1,0,0,0,1,0,01,0,0,1,0,0,0,0,1,01,0,0,1,0,0,0,0,0,01,0,0,0,1,1,1,1,1,01,0,0,0,1,1,1,1,0,01,0,0,0,1,1,1,0,1,11,0,0,0,1,1,1,0,0,01,0,0,0,1,1,0,1,1,11,0,0,0,1,1,0,1,0,01,0,0,0,1,1,0,0,1,01,0,0,0,1,1,0,0,0,01,0,0,0,1,0,1,1,1,11,0,0,0,1,0,1,1,0,01,0,0,0,1,0,1,0,1,01,0,0,0,1,0,1,0,0,01,0,0,0,1,0,0,1,1,01,0,0,0,1,0,0,1,0,01,0,0,0,1,0,0,0,1,11,0,0,0,1,0,0,0,0,11,0,0,0,0,1,1,1,1,01,0,0,0,0,1,1,1,0,01,0,0,0,0,1,1,0,1,01,0,0,0,0,1,1,0,0,01,0,0,0,0,1,0,1,1,01,0,0,0,0,1,0,1,0,01,0,0,0,0,1,0,0,1,01,0,0,0,0,1,0,0,0,01,0,0,0,0,0,1,1,1,11,0,0,0,0,0,1,1,0,01,0,0,0,0,0,1,0,1,11,0,0,0,0,0,1,0,0,11,0,0,0,0,0,0,1,1,01,0,0,0,0,0,0,1,0,01,0,0,0,0,0,0,0,1,01,0,0,0,0,0,0,0,0,00,1,1,1,1,1,1,1,1,00,1,1,1,1,1,1,1,0,00,1,1,1,1,1,1,0,1,00,1,1,1,1,1,1,0,0,00,1,1,1,1,1,0,1,1,00,1,1,1,1,1,0,1,0,00,1,1,1,1,1,0,0,1,00,1,1,1,1,1,0,0,0,00,1,1,1,1,0,1,1,1,00,1,1,1,1,0,1,1,0,00,1,1,1,1,0,1,0,1,00,1,1,1,1,0,1,0,0,00,1,1,1,1,0,0,1,1,00,1,1,1,1,0,0,1,0,00,1,1,1,1,0,0,0,1,00,1,1,1,1,0,0,0,0,00,1,1,1,0,1,1,1,1,00,1,1,1,0,1,1,1,0,00,1,1,1,0,1,1,0,1,00,1,1,1,0,1,1,0,0,00,1,1,1,0,1,0,1,1,00,1,1,1,0,1,0,1,0,00,1,1,1,0,1,0,0,1,10,1,1,1,0,1,0,0,0,10,1,1,1,0,0,1,1,1,00,1,1,1,0,0,1,1,0,00,1,1,1,0,0,1,0,1,10,1,1,1,0,0,1,0,0,00,1,1,1,0,0,0,1,1,00,1,1,1,0,0,0,1,0,10,1,1,1,0,0,0,0,1,00,1,1,1,0,0,0,0,0,00,1,1,0,1,1,1,1,1,10,1,1,0,1,1,1,1,0,00,1,1,0,1,1,1,0,1,00,1,1,0,1,1,1,0,0,10,1,1,0,1,1,0,1,1,00,1,1,0,1,1,0,1,0,00,1,1,0,1,1,0,0,1,00,1,1,0,1,1,0,0,0,00,1,1,0,1,0,1,1,1,10,1,1,0,1,0,1,1,0,00,1,1,0,1,0,1,0,1,10,1,1,0,1,0,1,0,0,00,1,1,0,1,0,0,1,1,00,1,1,0,1,0,0,1,0,00,1,1,0,1,0,0,0,1,00,1,1,0,1,0,0,0,0,10,1,1,0,0,1,1,1,1,00,1,1,0,0,1,1,1,0,00,1,1,0,0,1,1,0,1,00,1,1,0,0,1,1,0,0,00,1,1,0,0,1,0,1,1,10,1,1,0,0,1,0,1,0,10,1,1,0,0,1,0,0,1,00,1,1,0,0,1,0,0,0,00,1,1,0,0,0,1,1,1,00,1,1,0,0,0,1,1,0,00,1,1,0,0,0,1,0,1,00,1,1,0,0,0,1,0,0,00,1,1,0,0,0,0,1,1,00,1,1,0,0,0,0,1,0,00,1,1,0,0,0,0,0,1,00,1,1,0,0,0,0,0,0,00,1,0,1,1,1,1,1,1,00,1,0,1,1,1,1,1,0,00,1,0,1,1,1,1,0,1,00,1,0,1,1,1,1,0,0,00,1,0,1,1,1,0,1,1,00,1,0,1,1,1,0,1,0,00,1,0,1,1,1,0,0,1,00,1,0,1,1,1,0,0,0,00,1,0,1,1,0,1,1,1,00,1,0,1,1,0,1,1,0,00,1,0,1,1,0,1,0,1,00,1,0,1,1,0,1,0,0,00,1,0,1,1,0,0,1,1,00,1,0,1,1,0,0,1,0,00,1,0,1,1,0,0,0,1,00,1,0,1,1,0,0,0,0,10,1,0,1,0,1,1,1,1,00,1,0,1,0,1,1,1,0,00,1,0,1,0,1,1,0,1,00,1,0,1,0,1,1,0,0,10,1,0,1,0,1,0,1,1,00,1,0,1,0,1,0,1,0,00,1,0,1,0,1,0,0,1,10,1,0,1,0,1,0,0,0,00,1,0,1,0,0,1,1,1,10,1,0,1,0,0,1,1,0,10,1,0,1,0,0,1,0,1,00,1,0,1,0,0,1,0,0,00,1,0,1,0,0,0,1,1,10,1,0,1,0,0,0,1,0,00,1,0,1,0,0,0,0,1,00,1,0,1,0,0,0,0,0,10,1,0,0,1,1,1,1,1,00,1,0,0,1,1,1,1,0,00,1,0,0,1,1,1,0,1,00,1,0,0,1,1,1,0,0,00,1,0,0,1,1,0,1,1,00,1,0,0,1,1,0,1,0,00,1,0,0,1,1,0,0,1,00,1,0,0,1,1,0,0,0,10,1,0,0,1,0,1,1,1,00,1,0,0,1,0,1,1,0,00,1,0,0,1,0,1,0,1,00,1,0,0,1,0,1,0,0,00,1,0,0,1,0,0,1,1,00,1,0,0,1,0,0,1,0,00,1,0,0,1,0,0,0,1,00,1,0,0,1,0,0,0,0,10,1,0,0,0,1,1,1,1,10,1,0,0,0,1,1,1,0,10,1,0,0,0,1,1,0,1,00,1,0,0,0,1,1,0,0,00,1,0,0,0,1,0,1,1,10,1,0,0,0,1,0,1,0,00,1,0,0,0,1,0,0,1,00,1,0,0,0,1,0,0,0,10,1,0,0,0,0,1,1,1,00,1,0,0,0,0,1,1,0,00,1,0,0,0,0,1,0,1,00,1,0,0,0,0,1,0,0,00,1,0,0,0,0,0,1,1,00,1,0,0,0,0,0,1,0,10,1,0,0,0,0,0,0,1,00,1,0,0,0,0,0,0,0,00,0,1,1,1,1,1,1,1,10,0,1,1,1,1,1,1,0,00,0,1,1,1,1,1,0,1,10,0,1,1,1,1,1,0,0,00,0,1,1,1,1,0,1,1,00,0,1,1,1,1,0,1,0,00,0,1,1,1,1,0,0,1,00,0,1,1,1,1,0,0,0,00,0,1,1,1,0,1,1,1,00,0,1,1,1,0,1,1,0,10,0,1,1,1,0,1,0,1,10,0,1,1,1,0,1,0,0,00,0,1,1,1,0,0,1,1,00,0,1,1,1,0,0,1,0,00,0,1,1,1,0,0,0,1,00,0,1,1,1,0,0,0,0,00,0,1,1,0,1,1,1,1,00,0,1,1,0,1,1,1,0,00,0,1,1,0,1,1,0,1,00,0,1,1,0,1,1,0,0,00,0,1,1,0,1,0,1,1,10,0,1,1,0,1,0,1,0,10,0,1,1,0,1,0,0,1,00,0,1,1,0,1,0,0,0,00,0,1,1,0,0,1,1,1,00,0,1,1,0,0,1,1,0,00,0,1,1,0,0,1,0,1,00,0,1,1,0,0,1,0,0,00,0,1,1,0,0,0,1,1,00,0,1,1,0,0,0,1,0,00,0,1,1,0,0,0,0,1,00,0,1,1,0,0,0,0,0,00,0,1,0,1,1,1,1,1,00,0,1,0,1,1,1,1,0,00,0,1,0,1,1,1,0,1,10,0,1,0,1,1,1,0,0,00,0,1,0,1,1,0,1,1,00,0,1,0,1,1,0,1,0,00,0,1,0,1,1,0,0,1,00,0,1,0,1,1,0,0,0,10,0,1,0,1,0,1,1,1,10,0,1,0,1,0,1,1,0,00,0,1,0,1,0,1,0,1,00,0,1,0,1,0,1,0,0,10,0,1,0,1,0,0,1,1,00,0,1,0,1,0,0,1,0,00,0,1,0,1,0,0,0,1,00,0,1,0,1,0,0,0,0,10,0,1,0,0,1,1,1,1,00,0,1,0,0,1,1,1,0,00,0,1,0,0,1,1,0,1,10,0,1,0,0,1,1,0,0,00,0,1,0,0,1,0,1,1,00,0,1,0,0,1,0,1,0,00,0,1,0,0,1,0,0,1,00,0,1,0,0,1,0,0,0,00,0,1,0,0,0,1,1,1,10,0,1,0,0,0,1,1,0,00,0,1,0,0,0,1,0,1,10,0,1,0,0,0,1,0,0,00,0,1,0,0,0,0,1,1,00,0,1,0,0,0,0,1,0,00,0,1,0,0,0,0,0,1,10,0,1,0,0,0,0,0,0,00,0,0,1,1,1,1,1,1,00,0,0,1,1,1,1,1,0,00,0,0,1,1,1,1,0,1,10,0,0,1,1,1,1,0,0,00,0,0,1,1,1,0,1,1,00,0,0,1,1,1,0,1,0,00,0,0,1,1,1,0,0,1,00,0,0,1,1,1,0,0,0,00,0,0,1,1,0,1,1,1,00,0,0,1,1,0,1,1,0,00,0,0,1,1,0,1,0,1,00,0,0,1,1,0,1,0,0,10,0,0,1,1,0,0,1,1,00,0,0,1,1,0,0,1,0,10,0,0,1,1,0,0,0,1,00,0,0,1,1,0,0,0,0,10,0,0,1,0,1,1,1,1,10,0,0,1,0,1,1,1,0,10,0,0,1,0,1,1,0,1,00,0,0,1,0,1,1,0,0,00,0,0,1,0,1,0,1,1,10,0,0,1,0,1,0,1,0,00,0,0,1,0,1,0,0,1,00,0,0,1,0,1,0,0,0,10,0,0,1,0,0,1,1,1,00,0,0,1,0,0,1,1,0,00,0,0,1,0,0,1,0,1,00,0,0,1,0,0,1,0,0,00,0,0,1,0,0,0,1,1,00,0,0,1,0,0,0,1,0,10,0,0,1,0,0,0,0,1,00,0,0,1,0,0,0,0,0,00,0,0,0,1,1,1,1,1,00,0,0,0,1,1,1,1,0,00,0,0,0,1,1,1,0,1,00,0,0,0,1,1,1,0,0,00,0,0,0,1,1,0,1,1,00,0,0,0,1,1,0,1,0,10,0,0,0,1,1,0,0,1,10,0,0,0,1,1,0,0,0,10,0,0,0,1,0,1,1,1,00,0,0,0,1,0,1,1,0,10,0,0,0,1,0,1,0,1,00,0,0,0,1,0,1,0,0,10,0,0,0,1,0,0,1,1,10,0,0,0,1,0,0,1,0,10,0,0,0,1,0,0,0,1,10,0,0,0,1,0,0,0,0,00,0,0,0,0,1,1,1,1,00,0,0,0,0,1,1,1,0,00,0,0,0,0,1,1,0,1,00,0,0,0,0,1,1,0,0,00,0,0,0,0,1,0,1,1,00,0,0,0,0,1,0,1,0,10,0,0,0,0,1,0,0,1,00,0,0,0,0,1,0,0,0,00,0,0,0,0,0,1,1,1,10,0,0,0,0,0,1,1,0,00,0,0,0,0,0,1,0,1,10,0,0,0,0,0,1,0,0,00,0,0,0,0,0,0,1,1,00,0,0,0,0,0,0,1,0,00,0,0,0,0,0,0,0,1,00,0,0,0,0,0,0,0,0,0
(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)

x = 43, y = 11, rule = not-x-rule9b2o2b2o3b2o$8bo4b2o2bob2o5$3bo7b2o4bo23b2o$2bo7bo5bo8b2o5bo7bo$23bob2o4bo$b2o6b2o4b2o5bo3bo4bo3bo5b2o$o7bo6b2o5bo11bo6bo!

When that didn't work, I tried reversing the order - counting up from 000000000 to 111111111. Still nothing.
@RULE also-not-x-rule@TABLEn_states:2neighborhood:Mooresymmetries:none0,0,0,0,0,0,0,0,0,01,0,0,0,0,0,0,0,0,00,1,0,0,0,0,0,0,0,01,1,0,0,0,0,0,0,0,10,0,1,0,0,0,0,0,0,01,0,1,0,0,0,0,0,0,00,1,1,0,0,0,0,0,0,11,1,1,0,0,0,0,0,0,00,0,0,1,0,0,0,0,0,01,0,0,1,0,0,0,0,0,10,1,0,1,0,0,0,0,0,11,1,0,1,0,0,0,0,0,00,0,1,1,0,0,0,0,0,01,0,1,1,0,0,0,0,0,00,1,1,1,0,0,0,0,0,01,1,1,1,0,0,0,0,0,00,0,0,0,1,0,0,0,0,01,0,0,0,1,0,0,0,0,00,1,0,0,1,0,0,0,0,01,1,0,0,1,0,0,0,0,00,0,1,0,1,0,0,0,0,01,0,1,0,1,0,0,0,0,00,1,1,0,1,0,0,0,0,01,1,1,0,1,0,0,0,0,10,0,0,1,1,0,0,0,0,01,0,0,1,1,0,0,0,0,00,1,0,1,1,0,0,0,0,01,1,0,1,1,0,0,0,0,00,0,1,1,1,0,0,0,0,01,0,1,1,1,0,0,0,0,10,1,1,1,1,0,0,0,0,01,1,1,1,1,0,0,0,0,00,0,0,0,0,1,0,0,0,01,0,0,0,0,1,0,0,0,00,1,0,0,0,1,0,0,0,11,1,0,0,0,1,0,0,0,00,0,1,0,0,1,0,0,0,11,0,1,0,0,1,0,0,0,00,1,1,0,0,1,0,0,0,01,1,1,0,0,1,0,0,0,00,0,0,1,0,1,0,0,0,01,0,0,1,0,1,0,0,0,10,1,0,1,0,1,0,0,0,11,1,0,1,0,1,0,0,0,10,0,1,1,0,1,0,0,0,11,0,1,1,0,1,0,0,0,00,1,1,1,0,1,0,0,0,11,1,1,1,0,1,0,0,0,00,0,0,0,1,1,0,0,0,01,0,0,0,1,1,0,0,0,00,1,0,0,1,1,0,0,0,01,1,0,0,1,1,0,0,0,00,0,1,0,1,1,0,0,0,01,0,1,0,1,1,0,0,0,10,1,1,0,1,1,0,0,0,01,1,1,0,1,1,0,0,0,00,0,0,1,1,1,0,0,0,01,0,0,1,1,1,0,0,0,00,1,0,1,1,1,0,0,0,01,1,0,1,1,1,0,0,0,10,0,1,1,1,1,0,0,0,01,0,1,1,1,1,0,0,0,00,1,1,1,1,1,0,0,0,11,1,1,1,1,1,0,0,0,10,0,0,0,0,0,1,0,0,01,0,0,0,0,0,1,0,0,00,1,0,0,0,0,1,0,0,01,1,0,0,0,0,1,0,0,00,0,1,0,0,0,1,0,0,01,0,1,0,0,0,1,0,0,00,1,1,0,0,0,1,0,0,01,1,1,0,0,0,1,0,0,00,0,0,1,0,0,1,0,0,11,0,0,1,0,0,1,0,0,00,1,0,1,0,0,1,0,0,01,1,0,1,0,0,1,0,0,00,0,1,1,0,0,1,0,0,01,0,1,1,0,0,1,0,0,00,1,1,1,0,0,1,0,0,11,1,1,1,0,0,1,0,0,00,0,0,0,1,0,1,0,0,01,0,0,0,1,0,1,0,0,00,1,0,0,1,0,1,0,0,01,1,0,0,1,0,1,0,0,10,0,1,0,1,0,1,0,0,01,0,1,0,1,0,1,0,0,00,1,1,0,1,0,1,0,0,01,1,1,0,1,0,1,0,0,10,0,0,1,1,0,1,0,0,01,0,0,1,1,0,1,0,0,00,1,0,1,1,0,1,0,0,01,1,0,1,1,0,1,0,0,00,0,1,1,1,0,1,0,0,01,0,1,1,1,0,1,0,0,10,1,1,1,1,0,1,0,0,01,1,1,1,1,0,1,0,0,00,0,0,0,0,1,1,0,0,01,0,0,0,0,1,1,0,0,00,1,0,0,0,1,1,0,0,01,1,0,0,0,1,1,0,0,00,0,1,0,0,1,1,0,0,01,0,1,0,0,1,1,0,0,00,1,1,0,0,1,1,0,0,01,1,1,0,0,1,1,0,0,00,0,0,1,0,1,1,0,0,11,0,0,1,0,1,1,0,0,00,1,0,1,0,1,1,0,0,11,1,0,1,0,1,1,0,0,00,0,1,1,0,1,1,0,0,01,0,1,1,0,1,1,0,0,00,1,1,1,0,1,1,0,0,01,1,1,1,0,1,1,0,0,10,0,0,0,1,1,1,0,0,01,0,0,0,1,1,1,0,0,00,1,0,0,1,1,1,0,0,11,1,0,0,1,1,1,0,0,00,0,1,0,1,1,1,0,0,01,0,1,0,1,1,1,0,0,10,1,1,0,1,1,1,0,0,01,1,1,0,1,1,1,0,0,00,0,0,1,1,1,1,0,0,01,0,0,1,1,1,1,0,0,00,1,0,1,1,1,1,0,0,01,1,0,1,1,1,1,0,0,00,0,1,1,1,1,1,0,0,01,0,1,1,1,1,1,0,0,00,1,1,1,1,1,1,0,0,01,1,1,1,1,1,1,0,0,00,0,0,0,0,0,0,1,0,01,0,0,0,0,0,0,1,0,00,1,0,0,0,0,0,1,0,01,1,0,0,0,0,0,1,0,10,0,1,0,0,0,0,1,0,01,0,1,0,0,0,0,1,0,00,1,1,0,0,0,0,1,0,11,1,1,0,0,0,0,1,0,10,0,0,1,0,0,0,1,0,11,0,0,1,0,0,0,1,0,00,1,0,1,0,0,0,1,0,11,1,0,1,0,0,0,1,0,10,0,1,1,0,0,0,1,0,01,0,1,1,0,0,0,1,0,00,1,1,1,0,0,0,1,0,11,1,1,1,0,0,0,1,0,00,0,0,0,1,0,0,1,0,01,0,0,0,1,0,0,1,0,00,1,0,0,1,0,0,1,0,01,1,0,0,1,0,0,1,0,00,0,1,0,1,0,0,1,0,01,0,1,0,1,0,0,1,0,00,1,1,0,1,0,0,1,0,01,1,1,0,1,0,0,1,0,00,0,0,1,1,0,0,1,0,01,0,0,1,1,0,0,1,0,00,1,0,1,1,0,0,1,0,01,1,0,1,1,0,0,1,0,10,0,1,1,1,0,0,1,0,11,0,1,1,1,0,0,1,0,00,1,1,1,1,0,0,1,0,01,1,1,1,1,0,0,1,0,00,0,0,0,0,1,0,1,0,11,0,0,0,0,1,0,1,0,00,1,0,0,0,1,0,1,0,11,1,0,0,0,1,0,1,0,10,0,1,0,0,1,0,1,0,01,0,1,0,0,1,0,1,0,00,1,1,0,0,1,0,1,0,11,1,1,0,0,1,0,1,0,00,0,0,1,0,1,0,1,0,11,0,0,1,0,1,0,1,0,10,1,0,1,0,1,0,1,0,01,1,0,1,0,1,0,1,0,00,0,1,1,0,1,0,1,0,11,0,1,1,0,1,0,1,0,00,1,1,1,0,1,0,1,0,01,1,1,1,0,1,0,1,0,00,0,0,0,1,1,0,1,0,01,0,0,0,1,1,0,1,0,10,1,0,0,1,1,0,1,0,01,1,0,0,1,1,0,1,0,00,0,1,0,1,1,0,1,0,01,0,1,0,1,1,0,1,0,00,1,1,0,1,1,0,1,0,11,1,1,0,1,1,0,1,0,00,0,0,1,1,1,0,1,0,01,0,0,1,1,1,0,1,0,00,1,0,1,1,1,0,1,0,01,1,0,1,1,1,0,1,0,10,0,1,1,1,1,0,1,0,01,0,1,1,1,1,0,1,0,00,1,1,1,1,1,0,1,0,11,1,1,1,1,1,0,1,0,10,0,0,0,0,0,1,1,0,11,0,0,0,0,0,1,1,0,00,1,0,0,0,0,1,1,0,11,1,0,0,0,0,1,1,0,00,0,1,0,0,0,1,1,0,01,0,1,0,0,0,1,1,0,00,1,1,0,0,0,1,1,0,01,1,1,0,0,0,1,1,0,00,0,0,1,0,0,1,1,0,01,0,0,1,0,0,1,1,0,00,1,0,1,0,0,1,1,0,11,1,0,1,0,0,1,1,0,00,0,1,1,0,0,1,1,0,01,0,1,1,0,0,1,1,0,00,1,1,1,0,0,1,1,0,01,1,1,1,0,0,1,1,0,10,0,0,0,1,0,1,1,0,01,0,0,0,1,0,1,1,0,10,1,0,0,1,0,1,1,0,01,1,0,0,1,0,1,1,0,00,0,1,0,1,0,1,1,0,01,0,1,0,1,0,1,1,0,10,1,1,0,1,0,1,1,0,01,1,1,0,1,0,1,1,0,00,0,0,1,1,0,1,1,0,01,0,0,1,1,0,1,1,0,00,1,0,1,1,0,1,1,0,11,1,0,1,1,0,1,1,0,00,0,1,1,1,0,1,1,0,01,0,1,1,1,0,1,1,0,00,1,1,1,1,0,1,1,0,01,1,1,1,1,0,1,1,0,00,0,0,0,0,1,1,1,0,01,0,0,0,0,1,1,1,0,00,1,0,0,0,1,1,1,0,11,1,0,0,0,1,1,1,0,00,0,1,0,0,1,1,1,0,11,0,1,0,0,1,1,1,0,00,1,1,0,0,1,1,1,0,01,1,1,0,0,1,1,1,0,00,0,0,1,0,1,1,1,0,11,0,0,1,0,1,1,1,0,00,1,0,1,0,1,1,1,0,01,1,0,1,0,1,1,1,0,00,0,1,1,0,1,1,1,0,01,0,1,1,0,1,1,1,0,00,1,1,1,0,1,1,1,0,11,1,1,1,0,1,1,1,0,10,0,0,0,1,1,1,1,0,01,0,0,0,1,1,1,1,0,00,1,0,0,1,1,1,1,0,01,1,0,0,1,1,1,1,0,00,0,1,0,1,1,1,1,0,01,0,1,0,1,1,1,1,0,00,1,1,0,1,1,1,1,0,01,1,1,0,1,1,1,1,0,00,0,0,1,1,1,1,1,0,11,0,0,1,1,1,1,1,0,00,1,0,1,1,1,1,1,0,11,1,0,1,1,1,1,1,0,10,0,1,1,1,1,1,1,0,01,0,1,1,1,1,1,1,0,00,1,1,1,1,1,1,1,0,01,1,1,1,1,1,1,1,0,00,0,0,0,0,0,0,0,1,01,0,0,0,0,0,0,0,1,00,1,0,0,0,0,0,0,1,01,1,0,0,0,0,0,0,1,00,0,1,0,0,0,0,0,1,01,0,1,0,0,0,0,0,1,00,1,1,0,0,0,0,0,1,01,1,1,0,0,0,0,0,1,00,0,0,1,0,0,0,0,1,01,0,0,1,0,0,0,0,1,00,1,0,1,0,0,0,0,1,01,1,0,1,0,0,0,0,1,00,0,1,1,0,0,0,0,1,01,0,1,1,0,0,0,0,1,00,1,1,1,0,0,0,0,1,01,1,1,1,0,0,0,0,1,00,0,0,0,1,0,0,0,1,01,0,0,0,1,0,0,0,1,00,1,0,0,1,0,0,0,1,01,1,0,0,1,0,0,0,1,00,0,1,0,1,0,0,0,1,01,0,1,0,1,0,0,0,1,00,1,1,0,1,0,0,0,1,11,1,1,0,1,0,0,0,1,10,0,0,1,1,0,0,0,1,01,0,0,1,1,0,0,0,1,00,1,0,1,1,0,0,0,1,11,1,0,1,1,0,0,0,1,00,0,1,1,1,0,0,0,1,01,0,1,1,1,0,0,0,1,10,1,1,1,1,0,0,0,1,01,1,1,1,1,0,0,0,1,00,0,0,0,0,1,0,0,1,11,0,0,0,0,1,0,0,1,00,1,0,0,0,1,0,0,1,01,1,0,0,0,1,0,0,1,10,0,1,0,0,1,0,0,1,01,0,1,0,0,1,0,0,1,00,1,1,0,0,1,0,0,1,01,1,1,0,0,1,0,0,1,00,0,0,1,0,1,0,0,1,11,0,0,1,0,1,0,0,1,00,1,0,1,0,1,0,0,1,11,1,0,1,0,1,0,0,1,00,0,1,1,0,1,0,0,1,01,0,1,1,0,1,0,0,1,00,1,1,1,0,1,0,0,1,01,1,1,1,0,1,0,0,1,10,0,0,0,1,1,0,0,1,01,0,0,0,1,1,0,0,1,00,1,0,0,1,1,0,0,1,01,1,0,0,1,1,0,0,1,00,0,1,0,1,1,0,0,1,11,0,1,0,1,1,0,0,1,10,1,1,0,1,1,0,0,1,01,1,1,0,1,1,0,0,1,00,0,0,1,1,1,0,0,1,01,0,0,1,1,1,0,0,1,00,1,0,1,1,1,0,0,1,01,1,0,1,1,1,0,0,1,00,0,1,1,1,1,0,0,1,01,0,1,1,1,1,0,0,1,00,1,1,1,1,1,0,0,1,01,1,1,1,1,1,0,0,1,00,0,0,0,0,0,1,0,1,01,0,0,0,0,0,1,0,1,00,1,0,0,0,0,1,0,1,01,1,0,0,0,0,1,0,1,00,0,1,0,0,0,1,0,1,01,0,1,0,0,0,1,0,1,00,1,1,0,0,0,1,0,1,01,1,1,0,0,0,1,0,1,00,0,0,1,0,0,1,0,1,01,0,0,1,0,0,1,0,1,00,1,0,1,0,0,1,0,1,01,1,0,1,0,0,1,0,1,00,0,1,1,0,0,1,0,1,01,0,1,1,0,0,1,0,1,00,1,1,1,0,0,1,0,1,01,1,1,1,0,0,1,0,1,10,0,0,0,1,0,1,0,1,01,0,0,0,1,0,1,0,1,00,1,0,0,1,0,1,0,1,01,1,0,0,1,0,1,0,1,10,0,1,0,1,0,1,0,1,01,0,1,0,1,0,1,0,1,00,1,1,0,1,0,1,0,1,11,1,1,0,1,0,1,0,1,00,0,0,1,1,0,1,0,1,11,0,0,1,1,0,1,0,1,10,1,0,1,1,0,1,0,1,01,1,0,1,1,0,1,0,1,00,0,1,1,1,0,1,0,1,11,0,1,1,1,0,1,0,1,00,1,1,1,1,0,1,0,1,01,1,1,1,1,0,1,0,1,10,0,0,0,0,1,1,0,1,01,0,0,0,0,1,1,0,1,00,1,0,0,0,1,1,0,1,01,1,0,0,0,1,1,0,1,00,0,1,0,0,1,1,0,1,01,0,1,0,0,1,1,0,1,00,1,1,0,0,1,1,0,1,01,1,1,0,0,1,1,0,1,10,0,0,1,0,1,1,0,1,01,0,0,1,0,1,1,0,1,00,1,0,1,0,1,1,0,1,01,1,0,1,0,1,1,0,1,00,0,1,1,0,1,1,0,1,01,0,1,1,0,1,1,0,1,00,1,1,1,0,1,1,0,1,01,1,1,1,0,1,1,0,1,10,0,0,0,1,1,1,0,1,11,0,0,0,1,1,1,0,1,10,1,0,0,1,1,1,0,1,01,1,0,0,1,1,1,0,1,00,0,1,0,1,1,1,0,1,11,0,1,0,1,1,1,0,1,00,1,1,0,1,1,1,0,1,01,1,1,0,1,1,1,0,1,10,0,0,1,1,1,1,0,1,01,0,0,1,1,1,1,0,1,00,1,0,1,1,1,1,0,1,01,1,0,1,1,1,1,0,1,00,0,1,1,1,1,1,0,1,01,0,1,1,1,1,1,0,1,10,1,1,1,1,1,1,0,1,01,1,1,1,1,1,1,0,1,00,0,0,0,0,0,0,1,1,11,0,0,0,0,0,0,1,1,00,1,0,0,0,0,0,1,1,11,1,0,0,0,0,0,1,1,00,0,1,0,0,0,0,1,1,01,0,1,0,0,0,0,1,1,00,1,1,0,0,0,0,1,1,01,1,1,0,0,0,0,1,1,00,0,0,1,0,0,0,1,1,01,0,0,1,0,0,0,1,1,10,1,0,1,0,0,0,1,1,11,1,0,1,0,0,0,1,1,00,0,1,1,0,0,0,1,1,01,0,1,1,0,0,0,1,1,00,1,1,1,0,0,0,1,1,01,1,1,1,0,0,0,1,1,00,0,0,0,1,0,0,1,1,01,0,0,0,1,0,0,1,1,00,1,0,0,1,0,0,1,1,01,1,0,0,1,0,0,1,1,00,0,1,0,1,0,0,1,1,11,0,1,0,1,0,0,1,1,10,1,1,0,1,0,0,1,1,01,1,1,0,1,0,0,1,1,00,0,0,1,1,0,0,1,1,01,0,0,1,1,0,0,1,1,00,1,0,1,1,0,0,1,1,01,1,0,1,1,0,0,1,1,00,0,1,1,1,0,0,1,1,01,0,1,1,1,0,0,1,1,00,1,1,1,1,0,0,1,1,01,1,1,1,1,0,0,1,1,00,0,0,0,0,1,0,1,1,01,0,0,0,0,1,0,1,1,00,1,0,0,0,1,0,1,1,11,1,0,0,0,1,0,1,1,00,0,1,0,0,1,0,1,1,01,0,1,0,0,1,0,1,1,00,1,1,0,0,1,0,1,1,01,1,1,0,0,1,0,1,1,10,0,0,1,0,1,0,1,1,11,0,0,1,0,1,0,1,1,00,1,0,1,0,1,0,1,1,01,1,0,1,0,1,0,1,1,10,0,1,1,0,1,0,1,1,01,0,1,1,0,1,0,1,1,00,1,1,1,0,1,0,1,1,01,1,1,1,0,1,0,1,1,10,0,0,0,1,1,0,1,1,01,0,0,0,1,1,0,1,1,00,1,0,0,1,1,0,1,1,11,1,0,0,1,1,0,1,1,00,0,1,0,1,1,0,1,1,01,0,1,0,1,1,0,1,1,00,1,1,0,1,1,0,1,1,01,1,1,0,1,1,0,1,1,00,0,0,1,1,1,0,1,1,11,0,0,1,1,1,0,1,1,00,1,0,1,1,1,0,1,1,11,1,0,1,1,1,0,1,1,00,0,1,1,1,1,0,1,1,01,0,1,1,1,1,0,1,1,00,1,1,1,1,1,0,1,1,11,1,1,1,1,1,0,1,1,00,0,0,0,0,0,1,1,1,01,0,0,0,0,0,1,1,1,00,1,0,0,0,0,1,1,1,11,1,0,0,0,0,1,1,1,00,0,1,0,0,0,1,1,1,01,0,1,0,0,0,1,1,1,00,1,1,0,0,0,1,1,1,01,1,1,0,0,0,1,1,1,00,0,0,1,0,0,1,1,1,01,0,0,1,0,0,1,1,1,00,1,0,1,0,0,1,1,1,01,1,0,1,0,0,1,1,1,10,0,1,1,0,0,1,1,1,01,0,1,1,0,0,1,1,1,10,1,1,1,0,0,1,1,1,01,1,1,1,0,0,1,1,1,10,0,0,0,1,0,1,1,1,11,0,0,0,1,0,1,1,1,10,1,0,0,1,0,1,1,1,01,1,0,0,1,0,1,1,1,00,0,1,0,1,0,1,1,1,11,0,1,0,1,0,1,1,1,00,1,1,0,1,0,1,1,1,01,1,1,0,1,0,1,1,1,10,0,0,1,1,0,1,1,1,01,0,0,1,1,0,1,1,1,00,1,0,1,1,0,1,1,1,01,1,0,1,1,0,1,1,1,00,0,1,1,1,0,1,1,1,01,0,1,1,1,0,1,1,1,10,1,1,1,1,0,1,1,1,01,1,1,1,1,0,1,1,1,00,0,0,0,0,1,1,1,1,01,0,0,0,0,1,1,1,1,00,1,0,0,0,1,1,1,1,01,1,0,0,0,1,1,1,1,00,0,1,0,0,1,1,1,1,01,0,1,0,0,1,1,1,1,10,1,1,0,0,1,1,1,1,11,1,1,0,0,1,1,1,1,10,0,0,1,0,1,1,1,1,01,0,0,1,0,1,1,1,1,10,1,0,1,0,1,1,1,1,01,1,0,1,0,1,1,1,1,10,0,1,1,0,1,1,1,1,11,0,1,1,0,1,1,1,1,10,1,1,1,0,1,1,1,1,11,1,1,1,0,1,1,1,1,00,0,0,0,1,1,1,1,1,01,0,0,0,1,1,1,1,1,00,1,0,0,1,1,1,1,1,01,1,0,0,1,1,1,1,1,00,0,1,0,1,1,1,1,1,01,0,1,0,1,1,1,1,1,10,1,1,0,1,1,1,1,1,01,1,1,0,1,1,1,1,1,00,0,0,1,1,1,1,1,1,11,0,0,1,1,1,1,1,1,00,1,0,1,1,1,1,1,1,11,1,0,1,1,1,1,1,1,00,0,1,1,1,1,1,1,1,01,0,1,1,1,1,1,1,1,00,1,1,1,1,1,1,1,1,01,1,1,1,1,1,1,1,1,0

x = 77, y = 86, rule = also-not-x-rule31bobobobo$38bo$37b2o$36bo3$37bo$36b2o$27bobobobobo3$31bobobobo$38bo5bo$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$3bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$72bo3bo$73bob2o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo7$33bo$32b2o$3bobobobobobobobobobobobobobobo$bo$2bobobobobobobobobobobobobo$27bo$28bo5bo$29bo3b2o$2bobobobobobobobobobobobobobobobo2$bobobobo$8bo$7b2o!

Any idea what I'm doing wrong?
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: X-Rule

M. I. Wright wrote: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!

dvgrn
Moderator

Posts: 5718
Joined: May 17th, 2009, 11:00 pm

### Re: X-Rule

dvgrn wrote: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...
Last edited by M. I. Wright on October 6th, 2015, 10:01 pm, edited 1 time in total.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: X-Rule

dvgrn wrote: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:

@RULE x-rule@TABLEn_states:2neighborhood:Mooresymmetries: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'1,1,1,1,1,1,1,1,1,01,1,1,1,0,1,1,1,1,01,1,1,1,1,0,1,1,1,01,1,1,1,0,0,1,1,1,11,1,1,1,1,1,0,1,1,01,1,1,1,0,1,0,1,1,01,1,1,1,1,0,0,1,1,11,1,1,1,0,0,0,1,1,01,1,1,0,1,1,1,1,1,01,1,1,0,0,1,1,1,1,11,1,1,0,1,0,1,1,1,11,1,1,0,0,0,1,1,1,01,1,1,0,1,1,0,1,1,01,1,1,0,0,1,0,1,1,01,1,1,0,1,0,0,1,1,01,1,1,0,0,0,0,1,1,00,1,1,1,1,1,1,1,1,00,1,1,1,0,1,1,1,1,00,1,1,1,1,0,1,1,1,00,1,1,1,0,0,1,1,1,00,1,1,1,1,1,0,1,1,00,1,1,1,0,1,0,1,1,00,1,1,1,1,0,0,1,1,00,1,1,1,0,0,0,1,1,10,1,1,0,1,1,1,1,1,00,1,1,0,0,1,1,1,1,00,1,1,0,1,0,1,1,1,00,1,1,0,0,0,1,1,1,00,1,1,0,1,1,0,1,1,00,1,1,0,0,1,0,1,1,10,1,1,0,1,0,0,1,1,00,1,1,0,0,0,0,1,1,01,1,1,1,1,1,1,0,1,01,1,1,1,0,1,1,0,1,01,1,1,1,1,0,1,0,1,11,1,1,1,0,0,1,0,1,01,1,1,1,1,1,0,0,1,11,1,1,1,0,1,0,0,1,01,1,1,1,1,0,0,0,1,01,1,1,1,0,0,0,0,1,01,1,1,0,1,1,1,0,1,01,1,1,0,0,1,1,0,1,11,1,1,0,1,0,1,0,1,11,1,1,0,0,0,1,0,1,11,1,1,0,1,1,0,0,1,11,1,1,0,0,1,0,0,1,01,1,1,0,1,0,0,0,1,11,1,1,0,0,0,0,0,1,00,1,1,1,1,1,1,0,1,00,1,1,1,0,1,1,0,1,00,1,1,1,1,0,1,0,1,00,1,1,1,0,0,1,0,1,00,1,1,1,1,1,0,0,1,00,1,1,1,0,1,0,0,1,10,1,1,1,1,0,0,0,1,00,1,1,1,0,0,0,0,1,00,1,1,0,1,1,1,0,1,00,1,1,0,0,1,1,0,1,00,1,1,0,1,0,1,0,1,00,1,1,0,0,0,1,0,1,10,1,1,0,1,1,0,0,1,00,1,1,0,0,1,0,0,1,00,1,1,0,1,0,0,0,1,10,1,1,0,0,0,0,0,1,11,1,0,1,1,1,1,1,1,01,1,0,1,0,1,1,1,1,01,1,0,1,1,0,1,1,1,01,1,0,1,0,0,1,1,1,01,1,0,1,1,1,0,1,1,01,1,0,1,0,1,0,1,1,01,1,0,1,1,0,0,1,1,01,1,0,1,0,0,0,1,1,01,1,0,0,1,1,1,1,1,11,1,0,0,0,1,1,1,1,01,1,0,0,1,0,1,1,1,01,1,0,0,0,0,1,1,1,01,1,0,0,1,1,0,1,1,01,1,0,0,0,1,0,1,1,01,1,0,0,1,0,0,1,1,11,1,0,0,0,0,0,1,1,00,1,0,1,1,1,1,1,1,00,1,0,1,0,1,1,1,1,00,1,0,1,1,0,1,1,1,00,1,0,1,0,0,1,1,1,10,1,0,1,1,1,0,1,1,00,1,0,1,0,1,0,1,1,00,1,0,1,1,0,0,1,1,00,1,0,1,0,0,0,1,1,10,1,0,0,1,1,1,1,1,00,1,0,0,0,1,1,1,1,00,1,0,0,1,0,1,1,1,00,1,0,0,0,0,1,1,1,00,1,0,0,1,1,0,1,1,00,1,0,0,0,1,0,1,1,10,1,0,0,1,0,0,1,1,00,1,0,0,0,0,0,1,1,01,1,0,1,1,1,1,0,1,01,1,0,1,0,1,1,0,1,01,1,0,1,1,0,1,0,1,01,1,0,1,0,0,1,0,1,01,1,0,1,1,1,0,0,1,01,1,0,1,0,1,0,0,1,01,1,0,1,1,0,0,0,1,01,1,0,1,0,0,0,0,1,01,1,0,0,1,1,1,0,1,11,1,0,0,0,1,1,0,1,01,1,0,0,1,0,1,0,1,11,1,0,0,0,0,1,0,1,01,1,0,0,1,1,0,0,1,01,1,0,0,0,1,0,0,1,01,1,0,0,1,0,0,0,1,01,1,0,0,0,0,0,0,1,10,1,0,1,1,1,1,0,1,00,1,0,1,0,1,1,0,1,00,1,0,1,1,0,1,0,1,10,1,0,1,0,0,1,0,1,00,1,0,1,1,1,0,0,1,00,1,0,1,0,1,0,0,1,10,1,0,1,1,0,0,0,1,00,1,0,1,0,0,0,0,1,00,1,0,0,1,1,1,0,1,00,1,0,0,0,1,1,0,1,00,1,0,0,1,0,1,0,1,00,1,0,0,0,0,1,0,1,00,1,0,0,1,1,0,0,1,00,1,0,0,0,1,0,0,1,00,1,0,0,1,0,0,0,1,00,1,0,0,0,0,0,0,1,01,0,1,1,1,1,1,1,1,01,0,1,1,0,1,1,1,1,01,0,1,1,1,0,1,1,1,01,0,1,1,0,0,1,1,1,11,0,1,1,1,1,0,1,1,01,0,1,1,0,1,0,1,1,01,0,1,1,1,0,0,1,1,11,0,1,1,0,0,0,1,1,11,0,1,0,1,1,1,1,1,11,0,1,0,0,1,1,1,1,01,0,1,0,1,0,1,1,1,11,0,1,0,0,0,1,1,1,11,0,1,0,1,1,0,1,1,01,0,1,0,0,1,0,1,1,01,0,1,0,1,0,0,1,1,11,0,1,0,0,0,0,1,1,00,0,1,1,1,1,1,1,1,00,0,1,1,0,1,1,1,1,00,0,1,1,1,0,1,1,1,00,0,1,1,0,0,1,1,1,00,0,1,1,1,1,0,1,1,00,0,1,1,0,1,0,1,1,00,0,1,1,1,0,0,1,1,00,0,1,1,0,0,0,1,1,00,0,1,0,1,1,1,1,1,00,0,1,0,0,1,1,1,1,00,0,1,0,1,0,1,1,1,00,0,1,0,0,0,1,1,1,10,0,1,0,1,1,0,1,1,10,0,1,0,0,1,0,1,1,00,0,1,0,1,0,0,1,1,00,0,1,0,0,0,0,1,1,01,0,1,1,1,1,1,0,1,11,0,1,1,0,1,1,0,1,01,0,1,1,1,0,1,0,1,11,0,1,1,0,0,1,0,1,11,0,1,1,1,1,0,0,1,01,0,1,1,0,1,0,0,1,01,0,1,1,1,0,0,0,1,11,0,1,1,0,0,0,0,1,01,0,1,0,1,1,1,0,1,11,0,1,0,0,1,1,0,1,11,0,1,0,1,0,1,0,1,01,0,1,0,0,0,1,0,1,01,0,1,0,1,1,0,0,1,11,0,1,0,0,1,0,0,1,01,0,1,0,1,0,0,0,1,01,0,1,0,0,0,0,0,1,00,0,1,1,1,1,1,0,1,00,0,1,1,0,1,1,0,1,10,0,1,1,1,0,1,0,1,00,0,1,1,0,0,1,0,1,00,0,1,1,1,1,0,0,1,00,0,1,1,0,1,0,0,1,00,0,1,1,1,0,0,0,1,10,0,1,1,0,0,0,0,1,00,0,1,0,1,1,1,0,1,00,0,1,0,0,1,1,0,1,00,0,1,0,1,0,1,0,1,00,0,1,0,0,0,1,0,1,10,0,1,0,1,1,0,0,1,00,0,1,0,0,1,0,0,1,00,0,1,0,1,0,0,0,1,10,0,1,0,0,0,0,0,1,11,0,0,1,1,1,1,1,1,11,0,0,1,0,1,1,1,1,01,0,0,1,1,0,1,1,1,11,0,0,1,0,0,1,1,1,01,0,0,1,1,1,0,1,1,01,0,0,1,0,1,0,1,1,01,0,0,1,1,0,0,1,1,01,0,0,1,0,0,0,1,1,01,0,0,0,1,1,1,1,1,01,0,0,0,0,1,1,1,1,01,0,0,0,1,0,1,1,1,11,0,0,0,0,0,1,1,1,01,0,0,0,1,1,0,1,1,01,0,0,0,0,1,0,1,1,01,0,0,0,1,0,0,1,1,01,0,0,0,0,0,0,1,1,10,0,0,1,1,1,1,1,1,00,0,0,1,0,1,1,1,1,10,0,0,1,1,0,1,1,1,00,0,0,1,0,0,1,1,1,00,0,0,1,1,1,0,1,1,00,0,0,1,0,1,0,1,1,10,0,0,1,1,0,0,1,1,00,0,0,1,0,0,0,1,1,00,0,0,0,1,1,1,1,1,00,0,0,0,0,1,1,1,1,00,0,0,0,1,0,1,1,1,10,0,0,0,0,0,1,1,1,00,0,0,0,1,1,0,1,1,00,0,0,0,0,1,0,1,1,00,0,0,0,1,0,0,1,1,00,0,0,0,0,0,0,1,1,01,0,0,1,1,1,1,0,1,01,0,0,1,0,1,1,0,1,01,0,0,1,1,0,1,0,1,11,0,0,1,0,0,1,0,1,01,0,0,1,1,1,0,0,1,11,0,0,1,0,1,0,0,1,01,0,0,1,1,0,0,0,1,01,0,0,1,0,0,0,0,1,01,0,0,0,1,1,1,0,1,11,0,0,0,0,1,1,0,1,01,0,0,0,1,0,1,0,1,01,0,0,0,0,0,1,0,1,01,0,0,0,1,1,0,0,1,01,0,0,0,0,1,0,0,1,01,0,0,0,1,0,0,0,1,11,0,0,0,0,0,0,0,1,10,0,0,1,1,1,1,0,1,00,0,0,1,0,1,1,0,1,00,0,0,1,1,0,1,0,1,00,0,0,1,0,0,1,0,1,00,0,0,1,1,1,0,0,1,00,0,0,1,0,1,0,0,1,00,0,0,1,1,0,0,0,1,00,0,0,1,0,0,0,0,1,00,0,0,0,1,1,1,0,1,10,0,0,0,0,1,1,0,1,00,0,0,0,1,0,1,0,1,10,0,0,0,0,0,1,0,1,10,0,0,0,1,1,0,0,1,00,0,0,0,0,1,0,0,1,00,0,0,0,1,0,0,0,1,00,0,0,0,0,0,0,0,1,01,1,1,1,1,1,1,1,0,01,1,1,1,0,1,1,1,0,01,1,1,1,1,0,1,1,0,01,1,1,1,0,0,1,1,0,01,1,1,1,1,1,0,1,0,01,1,1,1,0,1,0,1,0,01,1,1,1,1,0,0,1,0,01,1,1,1,0,0,0,1,0,01,1,1,0,1,1,1,1,0,01,1,1,0,0,1,1,1,0,01,1,1,0,1,0,1,1,0,01,1,1,0,0,0,1,1,0,01,1,1,0,1,1,0,1,0,01,1,1,0,0,1,0,1,0,01,1,1,0,1,0,0,1,0,01,1,1,0,0,0,0,1,0,00,1,1,1,1,1,1,1,0,00,1,1,1,0,1,1,1,0,00,1,1,1,1,0,1,1,0,00,1,1,1,0,0,1,1,0,00,1,1,1,1,1,0,1,0,00,1,1,1,0,1,0,1,0,00,1,1,1,1,0,0,1,0,10,1,1,1,0,0,0,1,0,10,1,1,0,1,1,1,1,0,00,1,1,0,0,1,1,1,0,00,1,1,0,1,0,1,1,0,10,1,1,0,0,0,1,1,0,00,1,1,0,1,1,0,1,0,00,1,1,0,0,1,0,1,0,10,1,1,0,1,0,0,1,0,00,1,1,0,0,0,0,1,0,01,1,1,1,1,1,1,0,0,11,1,1,1,0,1,1,0,0,01,1,1,1,1,0,1,0,0,01,1,1,1,0,0,1,0,0,11,1,1,1,1,1,0,0,0,01,1,1,1,0,1,0,0,0,01,1,1,1,1,0,0,0,0,01,1,1,1,0,0,0,0,0,01,1,1,0,1,1,1,0,0,11,1,1,0,0,1,1,0,0,01,1,1,0,1,0,1,0,0,11,1,1,0,0,0,1,0,0,01,1,1,0,1,1,0,0,0,01,1,1,0,0,1,0,0,0,01,1,1,0,1,0,0,0,0,01,1,1,0,0,0,0,0,0,10,1,1,1,1,1,1,0,0,00,1,1,1,0,1,1,0,0,00,1,1,1,1,0,1,0,0,00,1,1,1,0,0,1,0,0,00,1,1,1,1,1,0,0,0,10,1,1,1,0,1,0,0,0,10,1,1,1,1,0,0,0,0,00,1,1,1,0,0,0,0,0,00,1,1,0,1,1,1,0,0,00,1,1,0,0,1,1,0,0,00,1,1,0,1,0,1,0,0,00,1,1,0,0,0,1,0,0,00,1,1,0,1,1,0,0,0,00,1,1,0,0,1,0,0,0,00,1,1,0,1,0,0,0,0,00,1,1,0,0,0,0,0,0,01,1,0,1,1,1,1,1,0,01,1,0,1,0,1,1,1,0,01,1,0,1,1,0,1,1,0,01,1,0,1,0,0,1,1,0,01,1,0,1,1,1,0,1,0,01,1,0,1,0,1,0,1,0,01,1,0,1,1,0,0,1,0,01,1,0,1,0,0,0,1,0,01,1,0,0,1,1,1,1,0,01,1,0,0,0,1,1,1,0,01,1,0,0,1,0,1,1,0,01,1,0,0,0,0,1,1,0,01,1,0,0,1,1,0,1,0,01,1,0,0,0,1,0,1,0,01,1,0,0,1,0,0,1,0,01,1,0,0,0,0,0,1,0,10,1,0,1,1,1,1,1,0,00,1,0,1,0,1,1,1,0,00,1,0,1,1,0,1,1,0,00,1,0,1,0,0,1,1,0,10,1,0,1,1,1,0,1,0,00,1,0,1,0,1,0,1,0,00,1,0,1,1,0,0,1,0,10,1,0,1,0,0,0,1,0,00,1,0,0,1,1,1,1,0,10,1,0,0,0,1,1,1,0,10,1,0,0,1,0,1,1,0,00,1,0,0,0,0,1,1,0,00,1,0,0,1,1,0,1,0,10,1,0,0,0,1,0,1,0,00,1,0,0,1,0,0,1,0,00,1,0,0,0,0,0,1,0,11,1,0,1,1,1,1,0,0,01,1,0,1,0,1,1,0,0,01,1,0,1,1,0,1,0,0,01,1,0,1,0,0,1,0,0,01,1,0,1,1,1,0,0,0,01,1,0,1,0,1,0,0,0,01,1,0,1,1,0,0,0,0,01,1,0,1,0,0,0,0,0,11,1,0,0,1,1,1,0,0,01,1,0,0,0,1,1,0,0,01,1,0,0,1,0,1,0,0,01,1,0,0,0,0,1,0,0,01,1,0,0,1,1,0,0,0,01,1,0,0,0,1,0,0,0,01,1,0,0,1,0,0,0,0,01,1,0,0,0,0,0,0,0,10,1,0,1,1,1,1,0,0,10,1,0,1,0,1,1,0,0,10,1,0,1,1,0,1,0,0,00,1,0,1,0,0,1,0,0,00,1,0,1,1,1,0,0,0,10,1,0,1,0,1,0,0,0,00,1,0,1,1,0,0,0,0,00,1,0,1,0,0,0,0,0,10,1,0,0,1,1,1,0,0,00,1,0,0,0,1,1,0,0,00,1,0,0,1,0,1,0,0,00,1,0,0,0,0,1,0,0,00,1,0,0,1,1,0,0,0,00,1,0,0,0,1,0,0,0,10,1,0,0,1,0,0,0,0,00,1,0,0,0,0,0,0,0,01,0,1,1,1,1,1,1,0,11,0,1,1,0,1,1,1,0,01,0,1,1,1,0,1,1,0,11,0,1,1,0,0,1,1,0,01,0,1,1,1,1,0,1,0,01,0,1,1,0,1,0,1,0,01,0,1,1,1,0,0,1,0,01,0,1,1,0,0,0,1,0,01,0,1,0,1,1,1,1,0,01,0,1,0,0,1,1,1,0,11,0,1,0,1,0,1,1,0,11,0,1,0,0,0,1,1,0,01,0,1,0,1,1,0,1,0,01,0,1,0,0,1,0,1,0,01,0,1,0,1,0,0,1,0,01,0,1,0,0,0,0,1,0,00,0,1,1,1,1,1,1,0,00,0,1,1,0,1,1,1,0,00,0,1,1,1,0,1,1,0,00,0,1,1,0,0,1,1,0,00,0,1,1,1,1,0,1,0,10,0,1,1,0,1,0,1,0,10,0,1,1,1,0,0,1,0,00,0,1,1,0,0,0,1,0,00,0,1,0,1,1,1,1,0,00,0,1,0,0,1,1,1,0,00,0,1,0,1,0,1,1,0,00,0,1,0,0,0,1,1,0,00,0,1,0,1,1,0,1,0,00,0,1,0,0,1,0,1,0,00,0,1,0,1,0,0,1,0,00,0,1,0,0,0,0,1,0,01,0,1,1,1,1,1,0,0,01,0,1,1,0,1,1,0,0,01,0,1,1,1,0,1,0,0,11,0,1,1,0,0,1,0,0,01,0,1,1,1,1,0,0,0,01,0,1,1,0,1,0,0,0,01,0,1,1,1,0,0,0,0,01,0,1,1,0,0,0,0,0,11,0,1,0,1,1,1,0,0,11,0,1,0,0,1,1,0,0,01,0,1,0,1,0,1,0,0,01,0,1,0,0,0,1,0,0,11,0,1,0,1,1,0,0,0,01,0,1,0,0,1,0,0,0,01,0,1,0,1,0,0,0,0,01,0,1,0,0,0,0,0,0,10,0,1,1,1,1,1,0,0,00,0,1,1,0,1,1,0,0,00,0,1,1,1,0,1,0,0,10,0,1,1,0,0,1,0,0,00,0,1,1,1,1,0,0,0,00,0,1,1,0,1,0,0,0,00,0,1,1,1,0,0,0,0,00,0,1,1,0,0,0,0,0,00,0,1,0,1,1,1,0,0,10,0,1,0,0,1,1,0,0,00,0,1,0,1,0,1,0,0,10,0,1,0,0,0,1,0,0,00,0,1,0,1,1,0,0,0,00,0,1,0,0,1,0,0,0,00,0,1,0,1,0,0,0,0,10,0,1,0,0,0,0,0,0,01,0,0,1,1,1,1,1,0,01,0,0,1,0,1,1,1,0,01,0,0,1,1,0,1,1,0,11,0,0,1,0,0,1,1,0,01,0,0,1,1,1,0,1,0,01,0,0,1,0,1,0,1,0,01,0,0,1,1,0,0,1,0,01,0,0,1,0,0,0,1,0,01,0,0,0,1,1,1,1,0,01,0,0,0,0,1,1,1,0,01,0,0,0,1,0,1,1,0,01,0,0,0,0,0,1,1,0,11,0,0,0,1,1,0,1,0,01,0,0,0,0,1,0,1,0,11,0,0,0,1,0,0,1,0,01,0,0,0,0,0,0,1,0,10,0,0,1,1,1,1,1,0,10,0,0,1,0,1,1,1,0,10,0,0,1,1,0,1,1,0,00,0,0,1,0,0,1,1,0,00,0,0,1,1,1,0,1,0,10,0,0,1,0,1,0,1,0,00,0,0,1,1,0,0,1,0,00,0,0,1,0,0,0,1,0,10,0,0,0,1,1,1,1,0,00,0,0,0,0,1,1,1,0,00,0,0,0,1,0,1,1,0,00,0,0,0,0,0,1,1,0,00,0,0,0,1,1,0,1,0,00,0,0,0,0,1,0,1,0,10,0,0,0,1,0,0,1,0,00,0,0,0,0,0,0,1,0,01,0,0,1,1,1,1,0,0,01,0,0,1,0,1,1,0,0,01,0,0,1,1,0,1,0,0,01,0,0,1,0,0,1,0,0,01,0,0,1,1,1,0,0,0,01,0,0,1,0,1,0,0,0,11,0,0,1,1,0,0,0,0,11,0,0,1,0,0,0,0,0,11,0,0,0,1,1,1,0,0,01,0,0,0,0,1,1,0,0,11,0,0,0,1,0,1,0,0,01,0,0,0,0,0,1,0,0,11,0,0,0,1,1,0,0,0,11,0,0,0,0,1,0,0,0,11,0,0,0,1,0,0,0,0,11,0,0,0,0,0,0,0,0,00,0,0,1,1,1,1,0,0,00,0,0,1,0,1,1,0,0,00,0,0,1,1,0,1,0,0,00,0,0,1,0,0,1,0,0,00,0,0,1,1,1,0,0,0,00,0,0,1,0,1,0,0,0,10,0,0,1,1,0,0,0,0,00,0,0,1,0,0,0,0,0,00,0,0,0,1,1,1,0,0,10,0,0,0,0,1,1,0,0,00,0,0,0,1,0,1,0,0,10,0,0,0,0,0,1,0,0,00,0,0,0,1,1,0,0,0,00,0,0,0,0,1,0,0,0,00,0,0,0,1,0,0,0,0,00,0,0,0,0,0,0,0,0,0

dvgrn
Moderator

Posts: 5718
Joined: May 17th, 2009, 11:00 pm

### Re: X-Rule

Oh, awesome! Glider guns GGa and GGb in RLE format:
x = 57, y = 7, rule = x-rule2o24b2o2b2o23b2o$bo24bo4bo23bo$6b2o12b2o15bo8bo2bo$5bo16bo13bo13bo$6b2o12b2o15bo8bo2bo$bo24bo4bo23bo$2o24b2o2b2o23b2o!
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: X-Rule

x = 4, y = 4, rule = x-ruleo$o$bo$2b2o! x = 9, y = 9, rule = x-rulebo$obo$obo4$6b2o$8bo$6b2o!

shifter
x = 3, y = 6, rule = x-ruleb2o3$2bo$bo$bo! If you're the person that uploaded to Sakagolue illegally, please PM me. x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

Posts: 3018
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: X-Rule

p2:

x = 5, y = 5, rule = x-rulebobo$o3bo2$o3bo$bobo! Splitters(?): x = 55, y = 8, rule = x-ruleo7bo37bo7bo$o7bo37bo7bo4$50bo$4bo44bobo$3bobo! Oscillators that follow an unknown (as of now) formula: x = 5, y = 7, rule = x-ruleo3bo$o3bo$2bo$bobo2$o3bo$o3bo!

x = 18, y = 40, rule = x-rule2o4b2o$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: x = 3, y = 5, rule = x-rule2bo$2bo$o$bo$bo! Last edited by danieldb on November 1st, 2015, 1:23 pm, edited 2 times in total. moved to drc danieldb Posts: 163 Joined: July 15th, 2015, 4:27 pm Location: Right behind you holding a knife ### Re: X-Rule Saka wrote: x = 4, y = 4, rule = x-ruleo$o$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.
Last edited by M. I. Wright on November 4th, 2015, 3:03 pm, edited 2 times in total.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: X-Rule

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

x = 12, y = 11, rule = x-rule7bobo$8bo$o$o7$10b2o!
moved to drc

danieldb

Posts: 163
Joined: July 15th, 2015, 4:27 pm
Location: Right behind you holding a knife

### Re: X-Rule

selfdestruct reflectors:

x = 7, y = 328, rule = x-rulebo3bo$bo3bo$3bo$2bobo3$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo9$o5bo$o5bo! moved to drc danieldb Posts: 163 Joined: July 15th, 2015, 4:27 pm Location: Right behind you holding a knife ### Re: X-Rule 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 correspond to the next neighborhoods: Best Regards -José Manuel Gómez Soto jmgomez Posts: 43 Joined: October 6th, 2015, 1:42 am ### Re: X-Rule A rake: x = 16, y = 27, rule = x-rule7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo$8bo4bo$10b2o3$10b2o$9bo2bo$2bo7b2o$bobo3b2o4b2o$5bob3o2b3o$o3b3obo4bobo$5bobo6bo$2bo7b2o2$8bo$8bo$6b2ob2o$8bo$8bo3$9bo2$8b2o! Another: x = 8, y = 9, rule = x-rulebobo$o$bobo2$3bo$bo$o$bo5bo$3bo!

And another:
x = 13, y = 4, rule = x-rulebo4bo4bo$obo2bobo2bobo2$10bobo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1822
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: X-Rule

A sideways only glider:

x = 4, y = 4, rule = x-rule3bo$bo$o$bobo! And 3 tagalongs: x = 18, y = 11, rule = x-rule15bo$15bo$13bo3bo2$7b3o4b3o$bo$bo2$bo6bo6bo$obo4bobo4bobo$obo4bobo4bobo! This is certainly an amazing rule moved to drc danieldb Posts: 163 Joined: July 15th, 2015, 4:27 pm Location: Right behind you holding a knife ### Re: X-Rule 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! jmgomez Posts: 43 Joined: October 6th, 2015, 1:42 am ### Re: X-Rule A for awesome wrote:A rake: x = 16, y = 27, rule = x-rule7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo$8bo4bo$10b2o3$10b2o$9bo2bo$2bo7b2o$bobo3b2o4b2o$5bob3o2b3o$o3b3obo4bobo$5bobo6bo$2bo7b2o2$8bo$8bo$6b2ob2o$8bo$8bo3$9bo2$8b2o! Another: x = 8, y = 9, rule = x-rulebobo$o$bobo2$3bo$bo$o$bo5bo$3bo!

And another:
x = 13, y = 4, rule = x-rulebo4bo4bo$obo2bobo2bobo2$10bobo!

Cool we can now create spaceships and puffers:

Ship called "Collider":

x = 34, y = 27, rule = x-rule7bobo2bobo4bobo2bobo$7bobo2bobo4bobo2bobo$6b2ob4ob2o2b2ob4ob2o$8bo4bo6bo4bo$8bo4bo6bo4bo$10b2o10b2o3$10b2o10b2o$9bo2bo8bo2bo$2bo7b2o10b2o7bo$bobo3b2o4b2o4b2o4b2o3bobo$5bob3o2b3o4b3o2b3obo$o3b3obo4bobo2bobo4bob3o3bo$5bobo6bo4bo6bobo$2bo7b2o10b2o7bo2$8bo16bo$8bo16bo$6b2ob2o12b2ob2o$8bo16bo$8bo16bo3$9bo14bo2$8b2o14b2o!

Domino Puffer:

x = 35, y = 30, rule = x-rule7bobo2bobo$7bobo2bobo$6b2ob4ob2o$8bo4bo6bobo2bobo$8bo4bo6bobo2bobo$10b2o7b2ob4ob2o$21bo4bo$21bo4bo$10b2o11b2o$9bo2bo$2bo7b2o$bobo3b2o4b2o8b2o$5bob3o2b3o7bo2bo$o3b3obo4bobo7b2o7bo$5bobo6bo5b2o4b2o3bobo$2bo7b2o8b3o2b3obo$19bobo4bob3o3bo$8bo11bo6bobo$8bo14b2o7bo$6b2ob2o$8bo17bo$8bo17bo$24b2ob2o$26bo$9bo16bo2$8b2o$25bo2$25b2o! Pre-Block Puffer: x = 52, y = 38, rule = x-rule37bobo2bobo$37bobo2bobo$36b2ob4ob2o$38bo4bo$38bo4bo$40b2o3$40b2o$39bo2bo$7bobo2bobo25b2o7bo$7bobo2bobo10bobo2bobo4b2o4b2o3bobo$6b2ob4ob2o9bobo2bobo4b3o2b3obo$8bo4bo10b2ob4ob2o2bobo4bob3o3bo$8bo4bo12bo4bo5bo6bobo$10b2o14bo4bo8b2o7bo$28b2o$43bo$10b2o31bo$9bo2bo15b2o11b2ob2o$2bo7b2o15bo2bo12bo$bobo3b2o4b2o5bo7b2o13bo$5bob3o2b3o4bobo3b2o4b2o$o3b3obo4bobo7bob3o2b3o$5bobo6bo3bo3b3obo4bobo8bo$2bo7b2o11bobo6bo$20bo7b2o12b2o$8bo$8bo17bo$6b2ob2o15bo$8bo15b2ob2o$8bo17bo$26bo2$9bo$27bo$8b2o$26b2o! Forward Rake: x = 52, y = 40, rule = x-rule37bobo2bobo$37bobo2bobo$19bobo2bobo9b2ob4ob2o$19bobo2bobo11bo4bo$18b2ob4ob2o10bo4bo$20bo4bo14b2o$20bo4bo$22b2o$40b2o$39bo2bo$22b2o16b2o7bo$21bo2bo12b2o4b2o3bobo$22b2o7bo5b3o2b3obo$7bobo2bobo4b2o4b2o3bobo3bobo4bob3o3bo$7bobo2bobo4b3o2b3obo8bo6bobo$6b2ob4ob2o2bobo4bob3o3bo6b2o7bo$8bo4bo5bo6bobo$8bo4bo8b2o7bo11bo$10b2o31bo$25bo15b2ob2o$25bo17bo$10b2o11b2ob2o15bo$9bo2bo12bo$2bo7b2o13bo$bobo3b2o4b2o27bo$5bob3o2b3o$o3b3obo4bobo8bo17b2o$5bobo6bo$2bo7b2o12b2o2$8bo$8bo$6b2ob2o$8bo$8bo3$9bo2$8b2o!
moved to drc

danieldb

Posts: 163
Joined: July 15th, 2015, 4:27 pm
Location: Right behind you holding a knife

### Re: X-Rule

jmgomez wrote: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
moved to drc

danieldb

Posts: 163
Joined: July 15th, 2015, 4:27 pm
Location: Right behind you holding a knife

### Re: X-Rule

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

M. I. Wright wrote: @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:

x = 4, y = 4, rule = x-rule2bo$2o$2b2o$bo! EDIT: added reference. Last edited by thunk on November 1st, 2015, 3:59 pm, edited 1 time in total. "What's purple and commutes? The Evanston Express." thunk Posts: 165 Joined: October 3rd, 2015, 8:50 pm Location: Central USA ### Re: X-Rule Nice!! -jm jmgomez Posts: 43 Joined: October 6th, 2015, 1:42 am ### Re: X-Rule Another P2: x = 6, y = 8, rule = x-rule4b2o$5bo$3bo$3b2o$b2o$2bo$o$2o!
▄▀
▀▀▀

Billabob

Posts: 143
Joined: April 2nd, 2015, 5:28 pm

### Re: X-Rule

jmgomez wrote: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.
"What's purple and commutes?
The Evanston Express."
thunk

Posts: 165
Joined: October 3rd, 2015, 8:50 pm
Location: Central USA

### Re: X-Rule

Thanks for you explain to me.

I get it!!

Thank you so much!!!

-jm
jmgomez

Posts: 43
Joined: October 6th, 2015, 1:42 am

### Re: X-Rule

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 '$' is a newline. So this: 2bo2$o3bo2$bobo$2bo!

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

The rule-table format is pretty straightforward as well. First comes the header:
@RULE <rulename>comments can go here, or included below if preceded by a #@TABLEn_states:2            #number of cell states. X-rule only has two (on and off), but Golly supports up to 256neighborhood:Moore    #self-explanatory. Other neighborhoods include vonNeumann and hexagonal

After that is the transitions. This is the format for a Moore neighborhood:
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:
8 1 27 s 36 5 4

For instance, the transition
0,1,1,1,0,1,1,0,0,1

means that in
1 1 10 0 11 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.
Last edited by M. I. Wright on November 1st, 2015, 6:20 pm, edited 1 time in total.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: X-Rule

M. I. Wright:

Best Regards
-jm
jmgomez

Posts: 43
Joined: October 6th, 2015, 1:42 am

### Re: X-Rule

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
jmgomez

Posts: 43
Joined: October 6th, 2015, 1:42 am

Next