I want to represent an order-5 square tiling (image from Wikipedia; more text below image):
Obviously for a simple grid I can uniquely refer to a given square by its
(x,y) position relative to the origin, in integer coordinates. To get to adjacent cells, one may simply increment or decrement
y. However, on the hyperbolic plane, things get messy, and it's unclear how to refer to a given cell.
Is there a better visual representation of the order-5 square tiling that would allow intuitive understanding of how to refer to individual cells, and failing that, is there a simple method to give each cell an index (such as
(x,y) for the Euclidean plane) that makes it easy to find its neighbors?