Tag Archives: Von Neumann neighborhood

Cellular automaton on quasiperiodic tiling

Any tiling can be used to define a cellular automaton. The tiles (squares, triangles, rhombs and other polygons) are simply the cells. Each tile has all other tiles with a common edge in its von Neumann neighborhood. I use the … Continue reading

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Cellular automation on the lattice of triangles

The tessellation of triangles can easily be mapped onto the square lattice, see the figures at the left and right. Upright triangles (colored green) and upside-down triangles (white) go into separate rows. The lines of interaction for the Von Neumann … Continue reading

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Hexagonal cellular automaton in color

The images from the hexagonal cellular automaton shown in “Basic parity rule – sample images  ” and “Modified parity rule – sample images ”  are only black and white. But I prefer color. To get similar images in color I modified the … Continue reading

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The parity rule on a hexagonal lattice

The MIT group of E. Fredkin, N. Margolus, T. Toffoli and G.Y. Vichniac has studied many cellular automata on the square lattice. We can use their ideas as recipes to run on the hexagonal lattice. Particularly simple is the parity … Continue reading

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Hexagonal cellular automata

Earlier I used a complicated cellular automaton to create images of snowflakes, see “Fake snowflakes“. It is based on a hexagonal grid in contrast to the well-known cellular automata such as Conway’s game of life, that use square grids. Here … Continue reading

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