Cellular Autamata on an Infinite Surface

Imagine a single cell in a huge grid of individuals, such as in a CGA (cellular genetic algorithm). In one generation the cell may crossover with any of its neighbors, but that is the limit of its involvement in the grid (barring some extra stuff going on like long distance links between cells or something). After two generations its genetic material may have spread a little farther, and it may get some material from a cell one more level away from. After 100 generations it will have interacted with cells 100 steps away.

But what if the grid is so large that each cell has some other cells that it never interacts with, even indirectly? What if the grid was infinitely large? In a non-strict language like Haskell we could even implement such a thing. We could start with some single cell in the middle (probably this would be a pointed grid, so we elect this "middle" cell to the the individual we focus on) and only instantiate (randomly) cells that we need to evaluate this cell each generation. After some number of generations, it will have forced the evaluation of a large space around it, but there will still be this infinitely of space- representing a grid of infinite interactions of genetic material. We could stop after 100 generations, say, and then search this grid forever, keeping track of the best individual we find. It would be an infinite space of solutions, with patches of fit ones that out competed the ones around them.

Admittedly there would be problems holding this in memory, as well as problems getting good individuals to evolve, with so much random material out there to interact with and no way to bound interaction except to out compete it (which is kind of cool by itself).

This is just some idea I had in class today, but I thought it was fun enough to post about. Could be fun to come back to one day, even if it never amounts to anything.