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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.

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2011 March 09

Breeders
These are not just breeders

image
Exploded diagram of Paul's SSS breeder.

To celebrate Paul Tooke's 50th birthday, this article is dedicated to one of his recent discoveries. Happy birthday, Paul!

Paul has recently been assembling patterns to defy common intuition about breeders, and thus help to determine a valid definition for what constitutes a breeder.

He has used the principles behind Gemini -- glider loops and universal construction -- to build unusual breeders with obscure properties. For example, he has engineered a SSS breeder, which amounts to a slide puffer (slide gun with stationary output) constructing more slide puffers. Moreover, he has designed it to have O(t^1.5) growth, rather than the O(n^2) typical of most breeders.

Paul's breeders, including a related SMS breeder, are available on the relevant forum thread. Rather than using the original Gemini construction arm, he has used an alternative construction arm known as the 'Pianola'. In the SMS version, this lays down block-laying switch engines; in the SSS version, this produces slide puffers instead.

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2009 February 28

Breeders
New pattern: LWSS breeder

Lucas Brown has constructed a new type of breeder, in which a rectangular array of high-period glider rakes moves eastward while producing gliders that crash to form p30 glider guns. Gliders from the p30 guns crash together in turn to produce streams of northbound spaceships. Lucas Brown's LWSS breeder

Here is the same breeder after 5000 generations -- the seventh LWSS factory has just begun to produce spaceships, and the component p30 glider guns in the eighth factory have started up but their gliders have not yet collided. Click this image for a closer view of the initial breeder pattern. LWSS breeder after 5000 ticks

2005 December 18

Breeders
Switch-engine breeder

2005-07-23-switch-breeder.rle

Switch-engine breeder: David Bell, 23 July 2005

Back in July, David Bell constructed a new switch-engine breeder. An orthogonal c/2 rake shoots gliders at the detritus left by a diagonal c/4 puffer, resulting in a 'natural' reaction that produces c/12 block-laying switch engines.