airesearcher

Having worked on nearly 500 complex lean libraries in math and theoretical physics, with AI assistance, I have some experience from the road to share here. In all my work I have found that AI is terrible at coming up with interesting ideas on its own - even the very best, latest models.

Without human scientific and mathematical intuition you can bet that AI will always take the road most travelled and miss the genuinely new and interesting breakthroughs - in fact it will not even think of them or try them without a human rider whipping it constantly to go down paths it would normally not consider.

And I think that is true in the case of the recent OpenAI blow-up -- it is alleged that even in this case AI did not come up with the winning technique without some human guidance.

I have never - across perhaps many thousands of chats with AI - seen AI push beyond the edge of what is known by itself, without being forced by a human to think outside the box.

I do think it might be possible to encode this process with prompting and agent orchestration methodologies - but even then - without a human - and human intuition - in the loop, I am skeptical.

Therefore I think a more accurate view of AI for math and science today is that it is an extremely powerful tool in the hands of a skilled operator with a strong intuition and roadmap of where to go, and rather boring when left to its devices.

Whether that will change in the future is a question. Nothing says that in principle AI could never do what a human driver does - but I still doubt that AI will replicate the life history and experience that real scientific and mathematical intuition is really made of.

AI trains on a lot of stuff - but it doesn't have hallway conversations, office-hours with teachers, or hard-won experience from all the things that failed that are NOT in the training data...

AI trains mainly on the record of what worked, not what didn't work and never even got published (and only lives in peoples heads) - and what didn't work is arguably as or more important for making breakthroughs and forming real intuition.

Looks better... the one thing I am not seeing is the behavior where they expand in two directions at the same time - but it might be that it's too small. Also it would be better if you started from a much lower density initial condition like 15% density. Also note - while Amazing Dragons shows really interesting behavior microscopically it is not the most balanced rule - there are other variants that are sparser and have a more interesting balance (see gallery, see repo to try them out). I found density of initial conditions is very important and different rules need different densities.

share a link to the new version of your shader - would love to check it out

perhaps also make a version that starts from random initial condition as well?

looks promising

Looks closer. Can’t tell from your example if exact.. but seems better

Very cool!

Actually - on that particular topic - you might want to read the articles and the math before forming an opinion - start from information geometry and fisher information metrics of information processing - which is what that particular line of thought is all about...Everything on that particular line of exploration is built up from fisher information where "consciousness" is defined as a high complexity information processing geometry and so its measurable. Because its defined as a measurable physical process, not as a magical quality, it's a mathematical argument. But of course that would require reading, and sufficient knowledge to understand it.

You're right that Realm of Lace edges are derived from node eligibility, making it theoretically equivalent to a complex multi-state CA. I've updated the documentation to reflect this honestly.

However, your Shadertoy port doesn't produce equivalent behavior to the original rule—I've tried several corrections in your shader and none match.

While you've demonstrated the theoretical point, this actually highlights why the abstraction matters: implementing these dynamics correctly is non-trivial even when the algorithm seems straightforward. The three-phase execution, metric calculations, and mutual eligibility create subtle interactions that are easy to get wrong.

Why the shader port doesn't work:

I've successfully implemented this same rule in Taichi (also GPU-based), and comparing the two reveals the issue.

The three-phase execution model requires intermediate storage between phases that Shadertoy's ping-pong buffer architecture can't provide.

In my Taichi implementation, each phase has its own buffer:

- Phase 1 reads node_degree (previous state) and writes to node_next_eligible

- Phase 2 reads node_next_eligible and writes to node_next_degree

- Phase 3 reads node_next_degree and writes back to node_degree

Shadertoy only has two buffers (previous frame read-only, current frame write-only), so the shader tries to collapse all three phases into one pass. But this breaks the execution model: when Phase 2 checks if a neighbor is eligible, it needs the neighbor's just-computed eligibility from Phase 1 of the current step, not the previous frame's data.

To properly implement this in a shader, you'd need either:

- A multi-pass setup with three separate render passes and intermediate textures

- Clever state packing to encode multiple values (eligibility + degree) in one buffer

The fact that the algorithm works correctly in Taichi but requires careful buffer management even on GPU demonstrates that "theoretical equivalence to traditional CA" doesn't mean "trivial to implement."

The three-phase execution model with intermediate states is a real architectural requirement, not just an abstraction.

Regarding edge rule tables: LACE has complete UI infrastructure for true edge-to-edge dynamics (edge states evolving based on connection patterns, independent of node eligibility).

The Rule Editor even has a full tab for it (which appears if a rule implements rule tables). But no rule implements the execution logic yet—it's a dormant feature that would provide the dynamic topology you're suggesting.

Thanks for pushing me to be more precise about all this though :)

The difference is that it is not merely using dynamic neighborhoods - it's using topological properties of neighbors and neighborhoods as metrics that rules use. For example, sum of degrees of neighbors, or betweenness, or other measures of networks. It's not, for example, simply using the links as virtual neighborhoods and modulating states over them.

Actually it's a pretty hard thing to implement - the main challenge was to make it performant in python... I had to jump through flaming hoops!

links are first-class entities. Some rules have cell states AND links. Some rules treat cell states as topological metrics of neighborhoods or neighbors. See the detailed .md cited above for more details.

Because I was too lazy to refactor it into a ton of modules...