Tlog(t) growth

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tlog(t) growth
tlog(t) growth image
Pattern type Miscellaneous
Number of cells 5685
Bounding box 635×377
Discovered by Dean Hickerson
Year of discovery 1990

tlog(t) growth is a pattern that was found by Dean Hickerson on November 13, 1990. It experiences infinite growth that is O(tlog(t)) and is the first such pattern that was constructed.

A bit more specifically, its population in generation t is asymptotic to tlog(t)/48. Even more specifically, for t ≥ 2, the population in generation 60×t is

Tlogt formula.gif

It uses a mechanism similar to Hickerson's primer; three breeders and two puffers create a sequence of large period guns so that the Nth gun has period 240N. In generation t there are about t/60 finished guns, which have emitted about t/(240*1) + t/(240*2) + t/(240*3) + ... + t/(240*(t/60)) ~ t log(t)/240 gliders.[1]

References

  1. Alan Hensel's lifep.zip pattern collection. Retrieved on August 9, 2009.