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2011 May 07

Restricted Patterns
Quadratic population growth from one row of cells

quadratic growth diagram
Quadratic growth pattern of width 1.
Stephen Silver, 20 April 2011.
Uses a breeder by Nick Gotts.
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.

1xN breeder after 2M ticks
The width-1 breeder after two million ticks, showing the first six switch engines
heading NW and SW, plus other stable and traveling detritus left over from
the construction process.
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.

2011-5-7-LWSS-recipe.rle LifeHistory diagram
Each LWSS is produced from a 4-glider construction reaction
designed to keep the LWSS streams and final breeder away from
the unavoidable patches of random ash and "junk" gliders.
The complete construction takes about a million generations.

1xN breeder after 2.5M ticks
The width-1 breeder after 2.5 million ticks, with ten switch engines visible.