{"id":45924264,"url":"https://github.com/micahbrun/continuous-complex-valued-cellular-automata","last_synced_at":"2026-02-28T09:01:14.599Z","repository":{"id":210323580,"uuid":"724805932","full_name":"MicahBrun/Continuous-Complex-Valued-Cellular-Automata","owner":"MicahBrun","description":"Continuous Complex-Valued Cellular Automata: Inspired by Lenia and quantum mechanics, this cellular automaton evolves according to the Schrödinger equation, with a convolutional Hamiltonian. 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The system is made up of a 2-D grid where each point stores a complex value. In the visualisation, the complex number is converted into a colour. The hue of the colour corresponds to the phase of the complex number; the brightness is proportional to the arctangent of the magnitude. \n\n## Theory\nThe system transforms according to:\n$$i \\frac{\\partial \\psi}{\\partial t} = h * \\psi$$\nWhere $h*\\psi$ represents the convolution of the functions $h$ and $\\psi$. $h$ is a real valued function while $\\psi$ may be complex valued.\n\nFrom this we can derive that:\n$$\\psi(t + \\Delta t) = \\mathrm{exp}(-i \\Delta t ~ h *) \\psi(t) $$\n\nIn the frequency domain, making use of the convolution theorem, this becomes:\n$$\\tilde{\\psi}(t + \\Delta t) = \\mathrm{exp}(-i \\Delta t ~ \\tilde{h}) \\tilde{\\psi}(t) $$\nWhere $\\tilde{f}$ represents the Fourier transform of a function.\n\n## Installation\n\nEnsure you have the following dependency installed before running the project:\n\n- [OpenCV](https://opencv.org/)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmicahbrun%2Fcontinuous-complex-valued-cellular-automata","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmicahbrun%2Fcontinuous-complex-valued-cellular-automata","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmicahbrun%2Fcontinuous-complex-valued-cellular-automata/lists"}