- What happens to CCA dynamics when the threshold is too high for
spiral formation, but not so high that wave fronts are convex confined?
Judging from a great many experiments on large arrays, there appears to
be a turbulent phase. (This name is only suggestive; we do not
claim any connection to classical fluid dynamics.)
- Roughly speaking, the system tries to make spiral centers, but these
would-be centers are unstable. As a result, when a vortex unravels it
leaves behind a smattering of debris that can act as a seed for the
formation of new wave fronts. This debris is a permanent and crucial part
of the dynamics. The turbulent phase is characterized by very large
length scales, so equilibrium behavior is only observed on sizable arrays.
Here we see the 8-color, range 2 Box, threshold 5 CCA on a 500 x 400
array after 2500 updates, started from a uniform random configuration.
I have felt for some time that these turbulent CCA equilibria make would
make nice fabric designs.
- For more about the mathematics behind Cyclic Cellular Automata, and
an extensive classification of their phenomenology, see R. Fisch,
J. Gravner and D. Griffeath, "Threshold-Range Scaling of Excitable
Cellular Automata." Statistics and Computing 1
(1991), 23-39. That article contains numerous color graphics, cutoff
tabulations, and phase diagrams for both CCA and GH dynamics.
- You can watch turbulent equiulibrium evolve for yourself by downloading
WinCA, our Windows-based interactive modeling environment for
cellular automata. To pick up the first beta version of WinCA look
in the kitchen sink. An experiment script
turbulen.xpt and bright 8-color palette turbulen.pal should
be added to the appropriate program subdirectories; these data files can
be found at the same location as the beta.