CAM6 VS WaveFunctionCollapse

Github Repo: https://github.com/SimHacker/CAM6/

https://www.youtube.com

I hate it when a program I wrote mocks me. In Lex Fridman's interview of Steven Wolfram, he demonstrates the machine learning functions in Mathematica by taking a photo of himself, which identifies him as a .... (I won't give it away):

https://www.youtube.com/watch?v=ez773teNFYA&t=2h20m05s

Here's a video I recently recorded of the CAM-6 simulator I implemented decades ago, and rewrote in JavaScript a few years ago.

https://www.youtube.com/watch?v=LyLMHxRNuck

I recorded that demo to show to Norman Margolus, who co-wrote the book and wrote the CAM6 PC Forth code and many rules, so it's pretty long and technical and starts out showing lots of code, but I'm sure you'll totally get and appreciate it. I linked to a pdf copy of the book in the comments, as well as the source code and playable app.

Demo of Don Hopkins' CAM6 Cellular Automata Machine simulator.

Live App: https://donhopkins.com/home/CAM6

Github Repo: https://github.com/SimHacker/CAM6/

Javacript Source Code: https://github.com/SimHacker/CAM6/blob/master/javascript/CAM...

PDF of CAM6 Book: https://donhopkins.com/home/cam-book.pdf

Comments from the code:

    // This code originally started life as a CAM6 simulator written in C

https://news.ycombinator.com/item?id=22738268

DonHopkins on March 31, 2020 | parent | context | favorite | on: Von Neumann Universal Constructor

Here's some stuff about that I posted in an earlier discussion, and transcribed from his book, "Theory of Self-Reproducing Automata".

His concept of self-reproducing mutating probabilistic quantum mechanical machine evolution is quite fascinating and terrifying at the same time (or outside of time), potentially much more powerful and dangerous than mere physical nanotechnology "gray goo" and universe-infesting self replicating von Neumann probes:

Can Programming Be Liberated from the von Neumann Style? (1977) [pdf] (thocp.net)

https://news.ycombinator.com/item?id=21855249

https://news.ycombinator.com/item?id=21858465

John von Neuman's 29 state cellular automata machine is (ironically) a classical decidedly "non von Neumann architecture".

https://en.wikipedia.org/wiki/Von_Neumann_cellular_automaton

He wrote the book on "Theory of Self-Reproducing Automata":

https://archive.org/details/theoryofselfrepr00vonn_0

He designed a 29 state cellular automata architecture to implement a universal constructor that could reproduce itself (which he worked out on paper, amazingly):

https://en.wikipedia.org/wiki/Von_Neumann_universal_construc...

He actually philosophized about three different kinds of universal constructors at different levels of reality:

First, the purely deterministic and relatively harmless mathematical kind referenced above, an idealized abstract 29 state cellular automata, which could reproduce itself with a Universal Constructor, but was quite brittle, synchronous, and intolerant of errors. These have been digitally implemented in the real world on modern computing machinery, and they make great virtual pets, kind of like digital tribbles, but not as cute and fuzzy.

https://github.com/SimHacker/CAM6/blob/master/javascript/CAM...

Second, the physical mechanical and potentially dangerous kind, which is robust and error tolerant enough to work in the real world (given enough resources), and is now a popular theme in sci-fi: the self reproducing robot swarms called "Von Neumann Probes" on the astronomical scale, or "Gray Goo" on the nanotech scale.

https://en.wikipedia.org/wiki/Self-replicating_spacecraft#Vo...

https://grey-goo.fandom.com/wiki/Von_Neumann_probe

>The von Neumann probe, nicknamed the Goo, was a self-replicating nanomass capable of traversing through keyholes, which are wormholes in space. The probe was named after Hungarian-American scientist John von Neumann, who popularized the idea of self-replicating machines.

Third, the probabilistic quantum mechanical kind, which could mutate and model evolutionary processes, and rip holes in the space-time continuum, which he unfortunately (or fortunately, the the sake of humanity) didn't have time to fully explore before his tragic death.

p. 99 of "Theory of Self-Reproducing Automata":

>Von Neumann had been interested in the applications of probability theory throughout his career; his work on the foundations of quantum mechanics and his theory of games are examples. When he became interested in automata, it was natural for him to apply probability theory here also. The Third Lecture of Part I of the present work is devoted to this subject. His "Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components" is the first work on probabilistic automata, that is, automata in which the transitions between states are probabilistic rather than deterministic. Whenever he discussed self-reproduction, he mentioned mutations, which are random changes of elements (cf. p. 86 above and Sec. 1.7.4.2 below). In Section 1.1.2.1 above and Section 1.8 below he posed the problems of modeling evolutionary processes in the framework of automata theory, of quantizing natural selection, and of explaining how highly efficient, complex, powerful automata can evolve from inefficient, simple, weak automata. A complete solution to these problems would give us a probabilistic model of self-reproduction and evolution. [9]

[9] For some related work, see J. H. Holland, "Outline for a Logical Theory of Adaptive Systems", and "Concerning Efficient Adaptive Systems".

https://www.deepdyve.com/lp/association-for-computing-machin...

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/5578...

https://www.worldscientific.com/worldscibooks/10.1142/10841

Ericson2314 3 months ago [-]

> Although I refer to conventional languages as "von Neumann languages" to take note of their origin and style, I do not, of course, blame the great mathematician for their complexity. In fact, some might say that I bear some responsibility for that problem.

From the paper. Whew.

Typically a cellular automata simulation will have some edge condition like wrapping or mirroring an adjacent cell.

A nice optimization trick is to make the cell buffers 2 cells wider and taller (or two times whatever the neighborhood radius is), and then before each generation you update the "gutter" by copying just the wrapped (or mirrored) pixels. Then your run the rule on the inset rectangle, and the code (in the inner loop) doesn't have to do bounds checking, and can assume there's a valid cell to read in all directions. That saves a hell of a lot of tests and branches in the inner loop.

Also, the Margolus neighborhood can be defined in terms of the Moore neighborhood + vertical phase (even/odd row) + horizontal phase (even/odd column) + time phase (even/odd time). Then you can tell if you're at an even or odd step, and which of the four squares of the grid you're in, to know what to do.

That's how the CAM6 worked in hardware: it used the x/y/time phases as additional bits of the index table lookup.

https://github.com/SimHacker/CAM6/blob/master/javascript/CAM...

Here's how my CAM6 emulator computes the Margolus lookup table index, based on the 9 Moore neighbors + phaseTime, phaseX, and phaseY:

                    function getTableIndexUnrotated(

Oh, nicely done! Trying to code up cellular automata simulations are pretty much guaranteed to push my brains through my nostrils - I've never progressed far beyond classic Conway. Your CAM6 library[1] may be about to steal my weekend from me!

[1] - https://github.com/SimHacker/CAM6

Thank you! And yes, I agree. I was looking at uh https://github.com/mxgmn/WaveFunctionCollapse and wondering if that were applicable here :)

Have a good day!

Intuitively, it measures the difference between two probability distributions. It's not symmetric, so it's not quite that, but in my opinion, it's good intuition.

As motivation, say you're an internet provider, providing internet service to a business. You naturally want to save money, so you perhaps want to compress packets before they go over the wire. Let's say the business you're providing service to also compresses their data, but they've made a mistake and do it inefficiently.

Let's say the business has, incorrectly, determined the probability distribution for their data to be $q(x)$. That is, they assign probability of seeing symbol $x$ to be $q(x)$. Let's say you've determined the "true" distribution to be $p(x)$. The entropy, or number of bits, they expect to transmit per packet/symbol will be $-\sum p(x) lg(q(x))$. Meaning, they'll compress their stream under the assumption that the distribution is $q(x)$ but the actually probability of seeing a packet, $x$, is $p(x)$, which is why the term $p(x) lg(q(x))$ shows up.

The number of bits you're transmitting is just $-\sum p(x) lg(p(x))$. Now we ask, how many bits, per packet, is the savings of your method over the businesses? This is $-\sum p(x) lg(q(x)/p(x))$, which is exactly the Kullback-Leibler divergence (maybe up to a sign difference).

In other words, given a "guess" at a distribution and the "true" distribution, how bad is it between them? This is the Kullback-Leibler distribution and why it shows up (I believe) in machine learning and fitness functions.

As a more concrete example, I just ran across a paper talking [0] about using WFC [1] to asses how well it, and other algorithms, do when trying to create generative "super mario brothers" like levels. Take a 2x2 or 3x3 grid, make a library of tiles, use that to generate a random level, then use the K-L divergence to determine how well your generative algorithm has done compared to the observed distribution from an example image.

[0] https://arxiv.org/pdf/1905.05077.pdf

[1] https://github.com/mxgmn/WaveFunctionCollapse

Reminds me of wave function collapse - a programmatic way to generate mazes.

I am using WFC to generate the terrain, with pretty much a copy-paste implementation of the original WFC implemented into Unity.

If you still want to go the WFC route, the original WFC repository is a great place to start. There's also a (relatively barebones looking) Godot plugin you could take a look at.

wave function collapse studies - this is done with the https://github.com/mxgmn/WaveFunctionCollapse algorithm after I saw https://github.com/CodingTrain/Wave-Function-Collapse mention it. done in P5! IG https://www.instagram.com/ronivonu/

There’s an interesting approach similar to this called [Wave Function Collapse](https://github.com/mxgmn/WaveFunctionCollapse) (no relation to wfc in physics idea besides inspiration). It can infer the probabilistic constraints from one input example, and it seems to generalize quite well. Here’s a [little demo](https://oskarstalberg.com/game/wave/wave.html)