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2006 May 12

Transcendental Objects
Quadratic Population Growth, Revisited

2006-03-11-Gotts-dots.rle
'Gotts Dots': sprouts its nth switchengine at t ~ 2^(24n-6) --
41 ON cells, growth rate O(t ln t)
Bill Gosper, 11 March 2006
Bill Gosper and Nick Gotts set some new records back in March, for patterns exhibiting quadratic growth starting from the smallest initial population. On March 11, Bill Gosper produced the starting configuration shown at right, which is closely related to patterns from his previous Golly experiments.

Golly screenshot of Nick Gotts' 'wedge' /  'GRoW'
26-cell quadratic growth pattern
Nick Gotts, 17 March 2006
A week later, based on this, Nick Gotts produced a 26-cell quadratic-growth pattern: a forward-glider-producing switch engine repeatedly overtakes a crystal formed by collision with sideways gliders produced by a c/12 rake assembly. When the switch engine reaches the crystal, a reaction produces a orthogonal block-laying switch engine and restarts the crystal production at the c/12 rake boundary.

Golly screenshot of 'wedge' /  'GRoW' at ~3.5M ticks
Here is what the 26-cell pattern looks like after ~3.5 million generations: