One cell thick pattern/Snippet

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A one cell thick pattern is a pattern that is only one cell thick; that is, it is contained entirely within one dimension of the Life plane. Put another way, it is a pattern with bounding box of the form y×1 for some natural number y. Because of their size restriction, exhaustive computer searches have been carried out to explore one cell thick patterns up to size about 40×1. Despite their inherent limitations, one cell thick patterns can exhibit quite complex behavior, even at reasonably small sizes.

In May 1998, Stephen Silver produced a one cell thick pattern that exhibits infinite growth, following a conjecture of Nick Gotts that such patterns exist. This pattern was extremely large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998, Paul Callahan performed an exhaustive computer search to find the following pattern that exhibits infinite growth. It is probably the most well-known one cell thick pattern, and Callahan showed that it is the smallest such one cell thick pattern (in terms of its bounding box) to exhibit infinite growth. It contains 28 alive cells and has a 39×1 bounding box.

Unidimensional infinite.png