Two-Dimensional Continuous Cellular Automata


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A two-dimensional continuous cellular automata is a cellular automata with two-dimension and has its output made into continuous ranged from 0 to 1. In this kind of cellular automata we draw the ouput in a figure by mapping the ouput into grayscale of a pixel on this figure. Like one-dimensional cellular automata, outputs of two-dimensional cellular automata vary as time goes by, and many interesting results have been observed, such as the famous special case of 2DCA, "The Life Game", "The Matrix". It can even produce a maze-like ouput, and furthermore, generate the maze-runner over the maze it produced. Using same idea we can make a cellular automata to recognize outputs of another cellular automata.

    It is known that cellular automata has the same computational power as Turing-machine. In my opinion, unless we have the ambition to find a brand new machine superior to Turing maching, it is important to categorize Turing machine into different classes. As we all know there are infinite number of Turing machine, and all computer scientists do is to find some machines that are feasible for their problems. Cellular automata obviously is a kind of machine that performs certain tasks properly. I believe that many mysteries are waiting for us to discove in cellular automata.