LACE - Link Automata Computing Engine

(written in python, with optional taichi GPU-powered mode for large-scale simulations)

LACE is a new kind of cellular automata where rules operate on cell states and their links to other cells.

Check out the Gallery in https://www.novaspivack.com/science/introducing-lace-a-new-k... to see the familiar Game of Life rule, but with links.

* Quick Examples **

Game of Life, with links: https://videopress.com/v/lTZ8e4hD

Amazing Dragons (LACE rules): https://videopress.com/v/lQ5Bghsj

** MANY more examples in the Gallery (in the blog post cited above)

Rules can use topological properties of cells and neighborhoods, such as number of connections, neighbor degree, and other metrics.

The added topological dimension enables rules that can have more interesting behavior than traditional "cells-only" CA rules, opening up a fascinating new computational world of new species of stable patterns - oscillators - gliders, puffers, and more.

For details on how these rules work, get the repo and open various rules in the rule editor, where all their parameters are explained. There are many new classes of rules to experiment with.

** You can get the repo and learn more at: https://github.com/novaspivack/lace

That's pretty darn cool.

How might you increase the overall order and decrease the chaos?

This is really cool, I wish they explained what the rules were; for example, the "Amazing Dragons" seems to self-organize very neatly, but I'm not really sure why it has that behavior.

Did you end up simulating the mouse brain after the LSD trip?

This is pretty cool. I have several points to make. 1. We all know that Cellular automata or more generally any dynamical system of sufficient complexity (and maybe not too much complexity) will be Turing complete, will have complicated "uncomputable" behavior, will have perhaps pattern formation, or gliders, solitons etc. So what is a valuable addition to this these computational investigations? I think when studying emergent computational behavior we really care about dynamics complexity / rules complexity. It's not impressive to get complicated dynamics out of a complicated system but the simplicity of game of life made it really impressive. I think in that regard LACE is pretty nice: the rule still feels very simple/natural and you can get much more structured/complex behavior with fewer cells.

2. Nevertheless in the end this blog shows mostly pretty pictures of computational, complex, emergent, chaotic behavior, which we've all seen before. And the key features that make the difference go something I would call physics-like are still missing. And I guess that would be complex stable patterns that can have complex stable interactions. Who knows maybe there are 10^16-celled patterns that have this but we don't know.

3. If I were you I would cut the whole preamble. It will make people take you less seriously than they should. You don't want to look like a crank.

So what actually is it? None of the rules in the videos look particularly striking compared to other Life-like cellular automata and 2d cellular automata in general. As you say, their behaviour includes oscillators, spaceships, patterns that grow endlessly... all things that are well-known from other cellular automata. So the videos didn't really show off why they're interesting.

I don't mind the rambling about "planets, galaxies, galaxy clusters, superclusters… and beyond …." but some technical detail would be nice too!

Game of life on a sphere could be nice. I never really liked how the gliders would just go off into nowhere.

Although I guess if we play with this too much there is a risk of inventing something like… Bloch's Game of Life or something.