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I am sure it could be the Belousov-Zhabotinsky reaction - but what is the mechanism? Something - an inhibitor perhaps - diffusing from the colonies? ...... Perhaps each apple (or part of an apple) is its own micro-environment.
In the center of the plate is a colony of Penicillium notatum, a mold that produces penicillin. After appearance of the mold colony, the plate was overlaid with a bacterial culture of Micrococcus luteus which forms a yellow "lawn" of growth. A zone of inhibition of bacterial growth surrounds the fungal colony where penicillin has diffused into the medium.
... rotate the fruit to see if sporulation can be driven at ninety degrees to the initial lines...
Today, Alan Turing is best known as the father of modern computer science, but in 1952 he sketched out a biological model in which two chemicals — an activator and an inhibitor — could interact to form the basis for everything from the color patterns of a butterfly’s wings to the black and white stripes of a zebra.
The Chemical Basis of Morphogenesis A. M. Turing... A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation ...