Chicken wire

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Chicken wire
Chicken wire image
Pattern type Agar
Period 1 (stable)
Discovered by Unknown
Year of discovery Unknown

Chicken wire is a stable agar of density 1/2. The "wires" can have any length at least 2, and they need not all be the same. As one of the first agars to be recognized, it was named after the type of fencing which it resembles wherein neighboring wires are twisted together to get a sort of hexagonal mesh.

Since agars are shift periodic configurations within the lattice of a cellular automaton, they exist in great numbers and varieties. To find them systematically, try restricting the scope of a search to only those of type (0,0,1) - no shift either vertically or horizontally after one generation. Then, a de Bruijn diagram can be constructed showing just those of vertical period 2 but with arbitrary horizontal structure. Doing so, they are found to fall into one or the other of three quite restricted classes: pure vacuum, Zebra stripes, or the Chicken wire. These are seen in the figure below:

The connected component of 0 is quite trivial, containing only the vacuum.
The connected component of 3 and C generates vertical zebra stripes, as seen in the lower example.
The remaining component alternates between arbitrarily long (but with at least one node) stretches of 5 or A (self-loops), with transitions passing through nodes 6 and 9.

That these patterns are taken from the de Bruijn diagram shows that they are the only ones possible. None of them (except vacuum) can be freestanding, nor can vertical zebra mix with chickenwire. And of course they can be rotated or reflected; horizontal and vertical are only relative.

The de Bruijn diagram 12x4 cells of the agar

External links