My thoughts precisely. Hopefully I've managed to interpret the rule correctly - if so, the the X-rule precursor in Alan Hensel's notation is B2eic3ic4rnj5ink/S12aen3c4qiyne5re6aei8. Let's call it x-rule-pre for short. Here's a ruletable:
Code: Select all
@RULE x-rule-pre
This rule is B2eic3ic4rnj5ink_S12aen3c4qiyne5re6aei8
It is an isotropic 'precursor' rule to a non-isotropic rule known as x-rule which has been shown to support logic universality by J.M. Gomez-Soto and A. Wuensche.
** NOTE ** This rule-table was incorrectly posted as the precursor to the x-rule. In fact it is very similar but the actual precursor rule additionally has S2i but not S3c.
[1] Gomez-Soto,JM., and A.Wuensche,“The X-rule: universal computation in a
non-isotropic Life-like Cellular Automaton”
*** File autogenerated by saverule. ***
This is a two state, isotropic, non-totalistic rule on the Moore neighbourhood.
The notation used to define the rule was originally proposed by Alan Hensel.
See http://www.ibiblio.org/lifepatterns/neighbors2.html for details.
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1}
var b={0,1}
var c={0,1}
var d={0,1}
var e={0,1}
var f={0,1}
var g={0,1}
var h={0,1}
# Birth
0,1,0,1,0,0,0,0,0,1
0,1,0,0,0,1,0,0,0,1
0,0,1,0,1,0,0,0,0,1
0,1,1,0,0,0,0,0,1,1
0,0,1,0,1,0,1,0,0,1
0,1,1,1,0,1,0,0,0,1
0,1,1,0,1,0,0,0,1,1
0,1,1,0,0,1,0,1,0,1
0,1,1,1,1,1,0,0,0,1
0,1,1,1,1,0,0,1,0,1
0,1,1,0,1,0,1,1,0,1
# Survival
1,1,0,0,0,0,0,0,0,1
1,0,1,0,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,0,1,0,0,0,1,0,0,1
1,0,1,0,1,0,1,0,0,1
1,1,1,1,0,0,1,0,0,1
1,1,1,0,1,1,0,0,0,1
1,1,1,0,1,0,1,0,0,1
1,1,1,0,1,0,0,0,1,1
1,1,0,1,0,1,0,1,0,1
1,1,1,0,1,1,1,0,0,1
1,1,1,0,1,0,1,0,1,1
1,1,1,1,1,1,1,0,0,1
1,1,1,1,1,0,1,0,1,1
1,1,1,0,1,1,1,0,1,1
1,1,1,1,1,1,1,1,1,1
# Death
1,a,b,c,d,e,f,g,h,0
This rule-table was incorrectly posted as the precursor to the x-rule. In fact it is very similar but the actual precursor rule additionally has S2i but not S3c. See the
for the correct rule table.
A lot of the simple patterns which don't rely on the non-isotropy of X-rule are of course common between the two rules. E.g. the orthogonal glider Gc and three tagalong's posted by danieldb (E/W as well as N/S), the diagonal glider Ga and extensions, the p2 and p6 oscillators, the reflector based oscillators and presumably many others.
There is a naturally occurring c/25 puffer (p50) which emits forward and backward streams of glider Gc (surely known by jmgomez?):
There are many possibilities for line puffers based on Gc. Here are a few: