Half-Distance Rules with Low Resolution

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In 1D cellular automata, totalistic half-distance rules can be displayed with a simple square, but much of their symmetry is lost. Some of the methods for showing their full symmetry are the shifted squares, hexagons, and disks methods. These display methods place an underlying cell between the two cells above, which is exactly what is needed when the radius is 1/2. For radii 3/2 and 5/2, the underlying cell is placed between the corresponding 4 or 6 cells.
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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA
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"Half-Distance Rules with Low Resolution"
http://demonstrations.wolfram.com/HalfDistanceRulesWithLowResolution/
Wolfram Demonstrations Project
Published: March 7 2011