Maximal Spanning Time for Neighborhood Growth on the Hamming Plane.

We consider a long-range growth dynamics on the two-dimensional integer lattice, initialized by a finite set of occupied points. Subsequently, a site x becomes occupied if the pair consisting of the counts of occupied sites along the entire horizontal and vertical lines through x lies outside a fixed Young diagram Z. We study the extremal quantity mu(Z), the maximal finite time at which the lattice is fully occupied. We give an upper bound on mu(Z) that is linear in the area of the bounding rectangle of Z, and a lower bound root s - 1, where s is the side length of the largest square contained in Z. We give more precise results for a restricted family of initial sets and for a simplified version of the dynamics.