# Polygonal Virtual Grids for CA Computing: Pentagonal, Hexagonal, and Octagonal Samplers

Polygonal Virtual Grids for CA Computing: Pentagonal, Hexagonal, and Octagonal Samplers

This Demonstration was motivated by a desire to circumvent the difficulty of constructing large arbitrary polygonal grids for use in cellular automata (CA) computing. Thus the goal of the Demonstration is threefold: (1) to show that given any desired grid-wide polygonal cell cluster shape (trigonal, rectangular, pentagonal, hexagonal, etc.) for use in CA computing, it is not necessary to a priori construct a starting grid that is populated with these polygonal cell clusters in order for the computation to meet its objective—rather, in concert with the right computing strategy, a CA neighborhood in the shape of the desired polygonal cell cluster shape achieves the same effect by way of a virtual grid; (2) to show that in light of (1), the starting grid size is limited only by acceptable computing speeds and can have the simplest possible shape; (3) to test the viability of (1) and (2) with a CA computation; here snowflake growth on a virtual hexagonal grid is shown to meet objective (3)—watch for enfolded growth in the direction of the six vertices (see thumbnail) as determined by the center of the hexagon and its vertices (see first snapshot; cf. second and third snapshots that show pentagonal and octagonal neighborhood vertices, respectively).

The methodology employed in this Demonstration could readily be extended to three-dimensional problems that call for polyhedral neighborhoods (where system-space can be a cube), and could otherwise be modified to let one engage single-body problems (car crashes, plate tectonics, etc., where multiple "localnhdAs" and whole-neighborhood updating is an effective approach).