- 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 The original version of our applet has now been replaced by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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