Generalized Wolfram Cellular Automata

Normal automata can only have states 0 or 1, but in this generalization, I interpolated the rules so that each cell can have a value in the range from 0 to 1. See this desmos graph: https://www.desmos.com/3d/80a93b4547 for a demonstration of how this interpolation is done for the case where only 4 rules define an automata instead of the normal 8 rules (so that the inputs and outputs can be visualized in 3D instead of 4D). In fact, with how this interpolation is defined, not only the cells, but also the rules need not be only binary values. An interpolated rule of this type would be a point in the higher-dimensional unit cube of R^8. But for this video, I used the rule 30 wolfram automata, so each individual rule's output is either 0 or 1. The output of this type of interpolation can be raised to a power in order to give it different characteristics (i.e. more of an affinity for smaller numbers or more of an affinity for larger numbers). See how the g(x, y) function in the desmos graph changes as n is varied for a demonstration of this fact. This video shows how the rule 30 cellular automata changes as the power to which it is raised goes from 0.001 to 10, with each frame (at 30FPS) corresponding to an increase of 0.001. The initial point on the graph has a value of 0.99999, as if the initial point of the automata was exactly equal to 1, it would behave exactly like a regular cellular automata. The changes are fairly gradual until the 1 minute mark (corresponding to a power of about 1.8), when it begins to be more chaotic. This chaos continues but eventually seems to settle more, especially after 4:42 (corresponding to about 8.45). I don't know what causes this behavior, but it is certainly interesting. As python (which the individual frames for this video was made in) uses 64-bit floating point numbers, the behavior towards the bottom of the graph may be due to imprecision rather than the actual behavior of such systems. This may not actually be the case, but especially with very large or small powers, small impressions can be significant. I might try using decimals in the future, which have arbitrary precision.