1×N quadratic growth

1×N quadratic growth
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Pattern type	Breeder
Number of cells	12599
Bounding box	1013783 × 1
Static symmetry	D2_+1
Discovered by	Stephen Silver
Year of discovery	2011
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Pattern files RLE 1xnquadraticgrowth.rle

1×N quadratic growth is a one-cell-thick pattern found by Stephen Silver on April 20, 2011. At N = 1013783, it is the first such pattern to exhibit quadratic growth. It uses the breeder from Nick Gotts' 26-cell quadratic growth, which is incrementally constructed by colliding LWSS streams travelling parallel to the baseline.

On November 6, 2014, Chris Cain completed a 14812 × 1 pattern that exhibits quadratic growth, and on November 9 he reduced this to 7242 × 1. The pattern was further reduced to 2596 × 1 allegedly in October 2015, but it was not reported until 2017.

As of October 2024, none of the 256 × 1 pseudorandom soups run by apgsearch under the "1x256" pseudosymmetry appear to exhibit quadratic growth.

Gallery

Generation 232 of Stephen Silver's 1×N quadratic growth, viewed at a scale of 220:1

x = 2596, y = 1, rule = B3/S23 6ob4o2b4o30b4ob9ob3ob3o112b4o3b12o3b3o139b3ob5ob4o5b5o71b3o2b5ob5o11b 4o6b7ob4o134b3o3b8o5b3ob4o19b5o2b3ob5ob7o58b4ob5ob3ob3o2b6o11b4o2b4ob 6ob3o61b3ob3o4b3ob7o181b4o4b3o3b9o19b3ob3o3b7o3b3o57b5ob5o2b3o112b3ob 4o2b3ob3ob9o62b4o4b4ob7o48b7o6b9o13b13ob3o2b4o90b3o6b5ob4ob6o3b6ob5o5b 5o53b11ob3o5b5o47b3ob3ob9ob4o277b3o3b8o5b3ob4o19b5o2b3ob5ob7o319b4o2b 4ob6ob3o61b3ob3o4b3ob7o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 800 ]] Chris Cain's 2596 × 1 quadratic growth pattern (click above to open LifeViewer) RLE: here Plaintext: here