I wonder what the most elegant Turing-complete universe is. I believe it to be a system based on collision-based computing [1]. My hunch is this: Matter and E

I wonder what the most elegant Turing-complete universe is. I believe it to be a system based on collision-based computing [1]. My hunch is this: Matter and Energy have a duality that is analogous to code and data. Einstein likened the speed of light to the speed of information. Wolfram/Toffoli/Fredkin or well, any other Cellular Automata specialist, studied the rate of propagation in CA, Lyapunov exponents. [2] Now it seems to me, that if we can create a digital system which provides for code <-> data duality analogous to Mass–energy equivalence [3], then we should be able to get stable structures that hold data, and stable processes that process data. I have tried for many years on and off with various CAs. Many of the CAs have been unconventional, like cells containing arrays of particles, particles being objects rather than simple numbers or enum types. And CAs based on reals or complex numbers or associated vector fields. --------------------------- Experiments https://github.com/churchofthought/ScatterLife https://github.com/churchofthought/ScatterLife (CUDA) https://github.com/churchofthought/HexagonalComplexAutomata https://github.com/churchofthought/HexagonalComplexAutomata (WebGL 2.0) https://github.com/churchofthought/Grautamaton https://github.com/churchofthought/Grautamaton (WebGL 2.0) --------------------------- Example of a Complex-valued Cellular Automata based on Sandpile dynamics Big Bang (video): https://photos.app.goo.gl/K7fovThbvatpmGQy5 https://photos.app.goo.gl/K7fovThbvatpmGQy5 End result (image): https://photos.app.goo.gl/n5amaqn8ZLVocn1Z6 https://photos.app.goo.gl/n5amaqn8ZLVocn1Z6 --------------------------- [1] https://link.springer.com/referenceworkentry/10.1007%2F978-3-540-92910-9_58 https://link.springer.com/referenceworkentry/10.1007%2F978-3... [2] https://www.math.ucdavis.edu/~gravner/papers/AUTOMATA2014_1509.pdf https://www.math.ucdavis.edu/~gravner/papers/AUTOMATA2014_15... [3] https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc...