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Continuous cellular automata with class 4 behavior

Examples of continuous cellular automata that exhibit class 4 behavior. The rules are of the same kind as in the previous picture, except that in the third case shown here, the gray level of each neighboring cell is multiplied by 1.13 before the average is done. In addition, the actual gray levels in these pictures are obtained by taking the difference between the gray level of each cell and its neighbor, thus removing the uniform stripes visible in the previous picture. It is remarkable that class 4 behavior with discrete localized structures can still occur in the continuous systems shown here.

Image Source Notebooks:

  • Wolfram Language source code for image on page 244

From Stephen Wolfram: A New Kind of Science [citation]