Abstract

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xshapesis a sort of super spirograph™. It is based primarily on rotational symmetry, although it can produce linear patterns. It was developed as an alternative way of viewing the output of Wolfram’s simple cellular automaton.[1]The algorithm uses the automaton to generate the contour bit-string that underlies each pattern. The algorithm requires four inputs:

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• the order of rotational symmetry of the shape (≥3)

• the cellular automaton rule (0-255) to be used to generate the contour bit-string 

• the length of the contour bit-string

• the number of steps of the cellular automaton to be executed

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Starting with either a standard or random initial contour bit-string,each step of the cellular automaton uses the result of the previous step as the input to the next. The programs offer a three-color display with 92 user-selectable palettes that have predefined combinations of line, fill, and background colors. The xshapesalgorithm is available in several different programs. One creates a series of images from randomly generated inputs. Another employs user-specified inputs to create images with particular desired characteristics. A third allows one input to be systematically varied while the others are held constant. This latter program generates a series of frames that can be assembled into a movie that illustrates the evolution of a cellular automaton from given initial conditions.