Log(t)^2 growth

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Log(t)2 growth
Log(t)2 growth image
Pattern type Miscellaneous
Number of cells 1431
Bounding box 290×218
Discovered by Dean Hickerson
Year of discovery 1992

Log(t)2 growth is a pattern that was found by Dean Hickerson on April 24, 1992. It experiences infinite growth that is O(log(t)2) and is the first such pattern that was constructed.

A bit more specifically, its population in generation n is asymptotic to (5log(t)2)/(3log(2)2). Even more specifically, for n ≥ 2, the population in generation 960×2n is 5n2/3 + 60n + 1875 + (100/9)*sin²(pi*n/3).

It is constructed out of a caber tosser, a modified block pusher, and a toggleable period 120 gun. Each glider from the caber tosser turns on the gun and causes the block pusher to go through one cycle (sending out a salvo and then waiting for the return gliders). When the cycle is complete, the gun is turned back off.[1]

See also

References

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