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Power Spectrum of Cellular Automaton Dynamics
Power Spectrum of Cellular Automaton Dynamics
The cellular automaton (CA) dynamics calculated from the total of each step can be seen as a kind of signal and analyzed by its power spectrum. The power spectrum found by the discrete Fourier transform of CA dynamics shows the amount of energy over time; it illustrates periodicities.
The elementary CA rules 0 and 255 (which represent class 1) evolve to a set of black or white cells at the first step. They maintain the behavior of a pulse in that the power spectrum is completely flat. This behavior can happen with other rules from class 1 or 2 depending on the initial condition.