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##### Restricted Patterns

Quadratic population growth from one row of cells

##### Restricted Patterns

Following up on an open problem he originally posed in 1998, Stephen Silver has constructed a minimal-height Life pattern that exhibits quadratic population growth -- a switch-engine breeder based on Nick Gotts' 26-cell quadratic-growth pattern, evolved from an initial pattern that's just a single cell in height. The other dimension could probably be optimized considerably, though -- the pattern is just slightly over a million cells in length (!), and takes a million ticks to evolve into the final breeder form.

At right is a diagram shows what the full pattern looks like, with a sample section of the generating line of cells expanded to explain the mechanism used to construct the breeder. Line sections are arranged to produce exactly-timed two-glider salvos, which collide to produce LWSSes, which in turn collide to build the breeder. A multi-step reaction at the X axis produces the second glider in each pair with an exactly-timed delay relative to the first one.

The breeder is based on Nick Gotts' 26-cell quadratic-growth pattern. It is incrementally constructed by colliding LWSS streams travelling parallel to the baseline.