- As advertised last week, here is the
next in a series of snapshots of self-organization at different locations
in the Larger than Life (LtL) phase space. This week's soup depicts
the range 12 Box rule with birth interval [200,300] and survival interval
[75,275], after about 40 updates started from a 50-50 random mix of live
and dead cells. The palette paints dead cells gray-blue, while recording the
time of the last birth at each live cell with a different color.
- In this rather substantial self-organizing regime, most of the lattice
is vacated after the first update, but isolated clouds of occupied sites remain.
Some of these clouds lack the necessary ingredients for self-organization and
so remain fixed; such speckled patches are seen in light blue.
(Just which magic ingredients are needed for further development remain
a mystery.) But a few clouds begin to consolidate at the second iteration and
'holes' are created. Iteration 3 leads to more occupied rings, some fairly
symmetric, others off-center. After that, the symmetric forms tend to either die
or make stable rings that cannot grow. A few such rings can be seen in shades of
violet and dark gray. But the asymmetric loops form expanding pretzels with more
and more cavities as time goes on. Eventually the nucleating pretzels interact
to incorporate the remaining isolated shapes, and a complex pseduo-random
equilibrium is attained. By this we mean that no local periodicity is observed
over protracted periods of time, while aggregate statistics of the steady-state
'seething gurp' are well-described by a space- and time- stationary
stochastic process.
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