Chapter 8: Implications for Everyday Systems

Section 4: Fluid Flow

Cellular automaton fluids

A large number of technical issues can be studied in connection with cellular automaton fluids. Many were already discussed in my original 1985 paper. Others have been covered in some of the many papers that have appeared since then. Of particular concern are issues about how rotation and translation invariance emerge at the level of fluid processes even though they are absent in the underlying cellular automaton structure. The very simplest rules turn out to have difficulties in these regards (see page 1024), which is why the model shown in the main text, for example, is on a hexagonal rather than a square grid (compare page 980). The model can be viewed as a block cellular automaton of the type discussed on page 460, but on a 2D hexagonal grid. In general a block cellular automaton works by making replacements for overlapping blocks of cells on alternating steps. In the 1D case of page 460, the blocks that are replaced consist of pairs of adjacent cells with two different alignments. On a 2D square grid, one can use overlapping 2×2 square blocks. But on a 2D hexagonal grid, one must instead alternate on successive steps between hexagons and their dual triangles.

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