And where, exactly, does it store the information that it has already searched an area? and how does it avoid dedicating resources to re-searching it?
https://en.m.wikipedia.org/wiki/Turing_pattern
> ... arises due to the interplay between differential diffusion (i.e., different values of diffusion coefficients) of chemical species and chemical reaction.
Meanwhile if you prune the apical bud to try to keep the tree small, it will just elect another leader and keep growing on a side branch.
I have a tree in my yard that got nibbled by insects when it was chest high. Killed the crown bud but not its two siblings. One of them won, then stood up straight and two years later you can barely tell.