The Cook Book
Recipe for the week of March 20 - 26
Critical Threshold Growth from a Large Box
- Last week we featured a linear random growth rule known as
Richardson's model. This week's offering depicts the nonlinear evolution of
a range 51 box Threshold Growth CA started from a 101 by 101 cell square
at time 0. Janko Gravner and I are currently studying the geometry of
minimal size nucleating droplets for Threshold Growth. The present
experiment is used to obtain upper bounds on the threshold for which
droplets of size s can nucleate in a threshold s rule.
- As it turns out, the central box here spreads without bound for
thresholds less than 4330, but fixates in a final finite configuration for
thresholds of 4330 or more. Our graphic displays the successively added
sites, each update in a new color, for the first 131 steps of the
threshold 4329 process. Note the complex pattern of layers as the droplet
evolves toward its asymptotic shape while trying to spread past the
corners of the original square. Later this spring we hope to offer a
corresponding lower bound graphic that will shed more light on the actual
geometry of critical minimal droplets.
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