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Beautiful Abelian Sandpiles

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Re: Beautiful Abelian Sandpiles

#3

Post by ggm »

Isn't this single frame state of a classic cellular automata? Note, not "just" because I mean no disrespect. I don't understand how this differs from Conway's life other than nuances of the live or die rule.

Re: Beautiful Abelian Sandpiles

#5

Post by [deleted] »

ggm wrote: post #3

Isn't this single frame state of a classic cellular automata? Note, not "just" because I mean no disrespect. I don't understand how this differs from Conway's life other than nuances of the live or die rule.

[deleted]

Re: Beautiful Abelian Sandpiles

#6

Post by gsf_emergency_6 »

ggm wrote: post #3

Isn't this single frame state of a classic cellular automata? Note, not "just" because I mean no disrespect. I don't understand how this differs from Conway's life other than nuances of the live or die rule.

CGL doesn't have the scale invariance ("fractality") of ASM. ASM criticality is stable and persistent. "fractal life on edge"?

what that looks like

https://youtu.be/rKD51IUNK3A?t=40s

Re: Beautiful Abelian Sandpiles

#7

Post by ggm »

gsf_emergency_6 wrote: post #6
ggm wrote: post #3

Isn't this single frame state of a classic cellular automata? Note, not "just" because I mean no disrespect. I don't understand how this differs from Conway's life other than nuances of the live or die rule.

CGL doesn't have the scale invariance ("fractality") of ASM. ASM criticality is stable and persistent. "fractal life on edge"? what that looks like https://youtu.be/rKD51IUNK3A?t=40s

So that gets to how it differs, but it doesn't say its not a cellular automata. It could say "it's a cellular automata with different rules"

Re: Beautiful Abelian Sandpiles

#8

Post by gsf_emergency_6 »

ggm wrote: post #7
gsf_emergency_6 wrote: post #6

Earlier quoted context omitted.

CGL doesn't have the scale invariance ("fractality") of ASM. ASM criticality is stable and persistent. "fractal life on edge"? what that looks like https://youtu.be/rKD51IUNK3A?t=40s

So that gets to how it differs, but it doesn't say its not a cellular automata. It could say "it's a cellular automata with different rules"

It is a cellular automata distinguished by commutativity. You used CGL as the basis for comparison, that's highly nonAbelian.

According to Wolfram (& I agree :), everything is a cellular automaton, so comparing to CGL made more sense to me.

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