One Dimensional Billiard Ball Diffusion Automata

[twinb7]

In a (long) blog post from February, Stephen Wolfram talked about the reversibility of the laws of physics, entropy, and - of course - drew comparisons with a cellular automata. Akin to the Margolus neighborhood, it is a one dimensional block CA with the following transition rules, which are reversible:

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x: a particle
o: a 'waiting' particle
_: a blank space
oo <-> xx
x_ <-> _x

This seems more convoluted than the obvious way of doing a billiard ball machine in one dimension (there is an additional 'waiting' particle), but the obvious way also doesn't produce interesting results. The rule table is below. States 1-3 are the 'left' of a block and states 4-6 are the 'right' of a block.

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@RULE WolframBBM

A one-dimensional billiard ball machine emulated with a block neighborhood.
Meant to be run with T(n,0).
1: Empty space, even (left)
2: Particle, even
3: Waiting particle, even
4: Empty space, odd (right)
5: Particle, odd
6: Waiting particle, odd

@TABLE
n_states:7
neighborhood:Moore
symmetries:none
var b={0,1,2,3,4,5,6}
var c={0,1,2,3,4,5,6}
var d={0,1,2,3,4,5,6}
var e={0,1,2,3,4,5,6}
var f={0,1,2,3,4,5,6}
var g={0,1,2,3,4,5,6}

var i={1,2,3}
var j={4,5,6}



#A pair of particles becomes a pair of waiting particles.
0,2,5,b,c,d,e,f,g,6
0,5,b,c,d,e,f,g,2,3

#A pair of waiting particles becomes a pair of particles.
0,3,6,b,c,d,e,f,g,5
0,6,b,c,d,e,f,g,3,2


#A particle and empty space exchange places.
0,2,4,b,c,d,e,f,g,4
0,4,b,c,d,e,f,g,2,2
0,5,b,c,d,e,f,g,1,1
0,1,5,b,c,d,e,f,g,5

#Otherwise, nothing changes
0,1,j,b,c,d,e,f,g,4
0,2,j,b,c,d,e,f,g,5
0,3,j,b,c,d,e,f,g,6
0,4,b,c,d,e,f,g,i,1
0,5,b,c,d,e,f,g,i,2
0,6,b,c,d,e,f,g,i,3

@COLORS
0 48 48 48
1 255 255 255 
2 255 0 0
3 255 128 0
4 255 255 255
5 255 0 0
6 255 128 0

And here is an example problem that demonstrates the 'diffusion' process. It also shows how the block neighborhood is emulated.

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x = 50, y = 1, rule = WolframBBM:T50,0
DADADADADADADADBEBEBEBEBEBEBEBEBEBEBDADADADADADADA!

The rule table has no consideration for the 'edge of the universe', so run this on a torus.

P.S. And a straightforward consequence of reversed pattern - notice what happens at gen 2842, apparently from randomness:

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x = 60, y = 1, rule = WolframBBM:T60,0
BEADAEBDAEADBEAEADAEAEADADADADAEBDADAEADADADADADBDCFBEAEAFCD!

[azulavoir]

I think the rule needs to be renamed. Wolfram makes Lifeviewer assume it's looking for a number after, like Wolfram110.

[confocaloid]

I think the rule needs to be renamed. Wolfram makes Lifeviewer assume it's looking for a number after, like Wolfram110.

I think that is not because of a name, but because nobody put the ruletable on the wiki. LifeViewer looks for a ruletable/rule tree in Rule:WolframBBM but there's no page there, so it says "Repository lookup failed with status 404".
E.g. the example pattern from the first post works with ruletable appended at the end:

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x = 50, y = 1, rule = WolframBBM:T50,0
DADADADADADADADBEBEBEBEBEBEBEBEBEBEBDADADADADADADA!

Edit: removed the inline ruletable which was here, since it is on LifeWiki now

[ilo Lisipo]

nobody put the ruletable on the wiki

I see no reason why NOT to put the ruletable on the wiki, so I did and it should work now.