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Local Growth in an Array of Disks

linear x variation
quadratic x variation
quadratic y variation
overall growth rate
size shading
Start with a closely packed array of identical disks. Then make each disk grow at a certain rate, attempting to maintain the packing. If the growth rate varies with the position of the disk, a packing can sometimes be maintained, and sometimes not. This setup provides a good model for processes in biology and elsewhere in which there is local isotropic growth at different rates in different positions. Failure to maintain the packing shown here would indicate that the real systemsay a growing plant leafwould somehow buckle into 3D.
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