The Cook Book

Recipe for the week of September 23 - 29

Replicating Bowties in HighLife

In this past summer's recipes of July 1 and July 15, we discussed replicators, certain finite configurations that evolve as exact fractals on the space- time lattice. Rather mysteriously, these exotic creatures are most frequently found in cellular automaton dynamics that are close-to-critical in their parameter spaces, at the proverbial 'edge of chaos.' This week's soup depicts perhaps my favorite replicator. Found in a variant of Conway's Game known as HighLife, I call it the bowtie pasta. HighLife's only distinction from the classic Life rule is that birth also occurs when a site has exactly 6 occupied neighbors.

As mentioned last July, a high-performace demo of the HighLife bowties is included in our WinCA software available from the Kitchen Sink. Of course a major advantage of the new Java language is platform independence. By minor tweaking of the Java By Example CA simulator mentioned two weeks ago, we created our first in-house applet. (You'll need a recent Java-enabled version of either Microsoft Internet Explorer or Netscape Navigator; links to both are found on the main Kitchen page.) The original version of our applet has now been replaced by Demo 2 of the Two-State Range 1 Automata applet in our CAffeine collection. Go run that experiment to see the bowtie pasta in action.

You might be asking: how does one discover these mysterious replicators amidst the inscrutable evolution of nonlinear dynamics? Experts of algorithmic search have found a few by ingenious reverse-time trajectory tracing, but for the most part they simply pop up from the initial noise of self-organizing CA systems. Indeed, this week's soup was captured from such experiments using WinCA. On an array with tens of thousands of cells I had to restart at least 50 times before a replicator emerged; but seek and ye shall find. The red and blue crystals were formed during the first few HighLife updates, whereas the disordered patch toward the lower left is a last remnant of 'seething gurp.'

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