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longitudinal, width 5

There is a fivefold symmetry, according to which the first eleven nodes shown below can be rotated by an arbitrary amount, giving 55 nodes altogether. The last three nodes are invariant to rotation, completing the total of 58 nodes shown in the table.

It is convenient to show only one member from each symmetry class, so the links between nodes need to indicate the amount of rotation or reflection implicit in the link.

0.2em

The simplest figure which can be constructed uses the lines of the first column above, just filling a square. It is ubiquitous; it might be named an ant. Although not self-propelled, it can be led by any live cell placed in front of it, or by a pair of live cells flanking it. Such cells can even be the hind feet of the ant in front, or of a pair of ants straddling it. Ants can even be staggered, although there is not enough room in a strip of width 5 for them to do anything but march in parallel. Nevertheless, space allowing, they frequently trail behind other configurations, sometimes leading still smaller processions.



Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx