One Dimensional Billiard Ball Diffusion Automata
Posted: December 21st, 2023, 11:41 pm
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:
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.
And here is an example problem that demonstrates the 'diffusion' process. It also shows how the block neighborhood is emulated.
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:
Code: Select all
x: a particle
o: a 'waiting' particle
_: a blank space
oo <-> xx
x_ <-> _xCode: Select all
@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 0Code: Select all
x = 50, y = 1, rule = WolframBBM:T50,0
DADADADADADADADBEBEBEBEBEBEBEBEBEBEBDADADADADADADA!
P.S. And a straightforward consequence of reversed pattern - notice what happens at gen 2842, apparently from randomness:
Code: Select all
x = 60, y = 1, rule = WolframBBM:T60,0
BEADAEBDAEADBEAEADAEAEADADADADAEBDADAEADADADADADBDCFBEAEAFCD!