- Happy New Year to all! This week's cooking uses a slick new
Web-based experimentation platform for one-dimensional cellular
automata that has been developed by Chris Langton, Howard Gutowitz, and the
folks at the Santa Fe Institute. Their simulator can be accessed from the
Artificial Life link in the Kitchen
Sink, or directly from
Exploring the Space of Cellular Automata. One can choose among 4 forms
(elementary, lambda, stochastic lambda, and complex) that generate space-time
images based on CA rules of increasing generality. Our soup was concocted
using the lambda form, with 8 colors, 640 cells, 480 time steps, a random
initial seed, and a range-two CA rule with a lambda value of approximately
0.3. One can also obtain a text file with the
exact rule specifications, although they are not terribly illuminating in
this case.
- In a nutshell, the lambda parameter provides a rule of thumb for
quantifying the complexity of CA rules on the integers. A celebrated
empirical scheme of Stephen Wolfram partitions such systems into four
Classes: I, II, III, and IV, according to their limiting (ergodic) behavior
from disordered initial states. Class IV rules are the rarest -- roughly,
those quasi-periodic dynamics that are delicately perched between order and disorder.
As Langton et al. explain, the lambda parameter can be tweaked to discover
ostensible Class IV rules with increased efficiency.
- From a mathematical point of view, I think it's fair to say that the
Wofram classification has never been precisely delineated, so there is
really no way of deciding definitively whether a given rule is Class IV.
Moreover, the classification was proposed largely on the basis of one-dimensional
experimentation, and the extent to which it extends to higher
dimensions is not at all clear. Indeed, some of the exotic self-organizational
phenomena documented here in the Kitchen seem to defy the
four categories. That said, the Langton-Gutowitz
Suggested Reading link is well worth pursuing.
And our soup just might be Class IV.
- I also like the Exploring page as a little preview of the much-touted
paradigm shift coming round the bend. Applets like this will be commonplace
real soon now, when Java reigns supreme, our PCs and workstations have all
been scrapped in favor of $50 Web boxes, we all enjoy infinite bandwidth,
and the Microsoft juggernaut finally crashes and burns...
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