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2013 January 19

New HighLife velocities

HighLife differs quantatively from Conway's Game of Life due to an additional birth condition: if a dead cell is surrounded by six live neighbours, it becomes alive. Qualitatively, the main difference between Life and HighLife is that the replicators in Life are imagined to be very large (no explicit examples have been discovered, although the technology behind Gemini could be adapted to yield one), whereas there is a nice small example in HighLife.

The HighLife replicator after thirty-six generations

Soon after the discovery of the replicator, it was realised that it could be tamed into a c/6 spaceship by pulling a blinker behind it. In 1999, Dean Hickerson proposed the existence of spaceships with much slower velocities, obtained by pushing junk at one end of a replicator track and pulling it at the other end. No explicit examples of spaceships were discovered this way, although Dean found a workable push reaction. This was mentioned on David Eppstein's website and in a chapter he wrote for Game of Life Cellular Automata.

It was pretty much forgotten for 14 years, until Adam P. Goucher wrote a search program to attempt to construct replicator tracks capable of forming spaceships. Initially, he found a c/69 spaceship with over 84 billion replicator units; his results and method of searching are summarised on Complex Projective 4-Space. Due to its immense size, slow movement and general appearance, it was named the Basilisk. Karel Suhajda commented on the post, suggesting trying different speeds. Tweaking the search parameters resulted in a c/63 spaceship with about 2 billion units; however, this was still prohibitively large for Golly.

Matthias Merzenich's (6,6) push reaction

Matthias Merzenich found a vastly more efficient push reaction, which moves a constellation by (6, 6) as opposed to Dean's (8,8) push. Adam P. Goucher did further alterations to incorporate this into the search program, which gave a c/24 Basilisk of just over 15000 replicator units. This is comfortably within the limitations of Golly, and there is an explicit RLE file of it. Using this technology, he proceeded to build c/24 glider rakes and even a gun to periodically emit c/24 Basilisks! A more comprehensive description and links to pattern files were posted on a later cp4space article.

A gun and a series of c/24 Basilisks emerging from it

Helmut Postl subsequently discovered a c/32 Basilisk, which is slightly smaller than its c/24 counterpart. Together with Matthias' c/5 diagonal spaceship from a couple of years ago, there are now twelve known spaceship velocities in HighLife: c/2, c/3, c/4, c/5 and 2c/5 orthogonal; c/4, c/5, c/6, c/24, c/32, c/63, c/69 diagonal. Additionally, Dean found a c/22 quadruple blinker-puffer by composing his (6,6) push with a (6,6) beacon pull, but it is unlikely that it can be exploited to yield further technology.

This all stems from the existence of the replicator in HighLife. If a similar construct were created in ordinary Life (proved to be possible), then similar XOR-extendable spaceships and so forth could be built. Dave Greene has been researching the possibilities in this direction.