Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

26 November 2013

New Technology from the Replicator Project

Now that the Conway's Life replicator pattern is in working order, what might the next step be?

The phase-shifted linear replicator isn't really a very satisfactory design. Each parent pattern can produce only one child pattern, which then blocks it from any further replication. It seems as if a quadratic-growth, space-filling replicator would be much more in keeping with von Neumann's (and Conway's) original purpose.

One major limitation of essentially linear designs like the Gemini spaceship and Geminoid replicator is that replication and movement perpendicular to the long stream of gliders is fairly easy, but it's very hard to make a new copy in the other direction -- just because it means constructing the far end of the new copy millions of cells away.

It's certainly not impossible to reach that far out into empty space with a constructor arm, but it's bound to be very slow -- either in terms of the absolute number of ticks, or in the amount of time that it takes to simulate a construction cycle. Even Golly's Hashlife algorithm has difficulty with very long streams of information-carrying gliders traveling next to each other in opposite directions -- the number of combinations goes up exponentially, and beyond a certain point no reasonable amount of memory can hold all the different hashtiles.

Luckily it may be possible to solve both of these problems at once with a diamond-shaped replicator. The memory loop would travel around the outside of a hollow square.

Hand blocks (or elbow blocks, if the UCs at the corners have two arms) can be trivially constructed in the correct starting locations by colliding LWSSes from one corner with gliders from an adjacent corner; glider pairs or slow salvos following the first glider will immediately have a target to work with.

To give Hashlife as much help as possible, it will make sense to adjust the reflection timings at the four corners so that the memory loop takes 2^N ticks per cycle; the spatial periodicity should also be a power of two.

The result will be a space-filling Life replicator with the same quadratic growth rate as Langton's Loops. It will be interesting to see how much memory will be needed to allow Golly to "run away" with the replicator simulation.

In the diagram at right, blue diamonds represent glider memory loops containing construction information. (A closed loop may not actually be needed, but that's another story.) Green objects are universal constructors and reflectors. The yellow arrows are eater groups that can absorb child replicators' attempts to build on top of a quiescent parent replicator. The white lines show the paths of starter LWSSes and construction gliders. The red numbers show replicators' generation number.

The New Technology

A number of the new construction and destruction mechanisms from the Geminoid project may be useful here: