Game of Life News

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.

Continue reading "Quadratic population growth from one row of cells"

Posted by Dave Greene at 00:33 | Permalink

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.

Continue reading "These are not just breeders"

Posted by Adam P. Goucher at 18:22 | Permalink

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.

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.

Posted by Dave Greene at 22:31 | Permalink

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.

Posted by Dave Greene at 15:36 | Permalink