Tlog(t) growth

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tlog(t) growth
x = 635, y = 377, rule = B3/S23 40bo13bo$39b3o11b3o$38b2obo5bo4b2obo$38b3o5b3o3b3o$39b2o4bo2b2o3b2o$ 45b2ob2o38b3o11b3o$44b3o2bo37bo2bo10bo2bo$45b2obo41bo4b3o6bo$46bo43bo 4bo2bo5bo$39b3o4bo3bo36bobo4bo3bo2bobo$39bo2bo3bo47b4o$39bo6bo48bo$39b o6b2obo$40bobo6b2o52bo$102b3o$44b2o48b3o4b2obo$46bo48b2o4b3o$48bo46b2o 5b2o$48bo7bo38b2ob2o$45bobo7b3o38bobo$46bo7b2obo39bo$54b3o$55b2o$86b3o $61bo5bo17bo2bo$60b3o3b3o19bo$59b2obo3bob2o18bo$59b3o5b3o15bobo$54bo5b 2o5b2o$52bobo20b3o3b3o6b2o$53b2o9bo10bo2bobo2bo6b3o$63b3o9bo7bo6b2o$ 75bo7bo8bo$63bobo10bobobobo$64bo$79bo$78b3o$28bo13bo34b2ob2o$27b3o11b 3o17b3ob3o10b3o$27bob2o4bo5bob2o18bobo12b3o$28b3o3b3o5b3o33b3o$28b2o3b 2o2bo4b2o34bobo$35b3o25b3o12bobo19b3o11b3o$59bo19bo20bo2bo10bo2bo$57bo bo25bobo12bo6b3o4bo$58b2o25b2o13bo5bo2bo4bo$41b3o42bo14bobo2bo3bo4bobo $40bo2bo61b2o2bobo$43bo63bo$43bo64b2obo$40bobo58bo6b3o$32b2o66b3o5b3o$ 32b2o26b2o38bob2o4b2o$43b3o3b3o8b2ob2o36b3o4bobo$26bo16bo2bobo2bo6bo 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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.