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Hi,

Does anyone know if there are some rules in Conwas' GoL or in automatas with higher amount of states that could be used to simulate the preservation of momentum somewhat correctly as in Newtonian physics?
https://en.wikipedia.org/wiki/Momentum

So my idea is to create a 2D cellular automata where the user could identify the objects and their velocity and mass and then observe as they move in the automata and collide.

1. The objects could move in the same direction in the same axis and then lose/gain velocity when they collide.
2. move in many directions and lose/gain velocity depending on the angle.
3. have friction with the plane so that their velocities would slow regardless of collisions.

Parts 2 and 3 are nice but also I am interested if someone have just created something to satisfy the part 1.


Thank you!

This is an intriguing concept, no doubt, but I think you are hitting on a very difficult problem to solve.

The "conserve momentum" bit is actually pretty easy (trivially easy from the physics point of view, relatively easy from a computational perspective), but the "meat" of this problems lies here: Recognizing adjacent cells in a cellular automaton as "belonging together" in an object (like a Glider) is highly non-trivial, to say the least.

It's actually one of the harder problems of cybernetics research ("how do human brains recognize that certain 'pixels' on the retina belong together to form a solid object?") and I would imagine that this is were the main problems of your approach will lie: To teach your program to recognize "contiguous objects" across several cells (which, for all intents and purposes, are independent from one another).

I am not aware if there is a ruleset that captures momentum conservation, but that does not mean that there isn't one (my knowledge is limited). So you might be lucky and someone more knowledgeable will point you in the right direction (or maybe even to the solution to your idea).

Again: Intriguing, for sure, but very likely not easily solved.

Thanks for the reply! Yeah it is kinda clear that it can be done as the physics itself is simple, but the actual implementation with simple rules and with a small neighbourhood like Moore's. I mean probably possible to do with very comples rules and a huge neighbourhood. One of my final interests for this would be to see a game where (almost) everything works just by simple cellular automata rules.