Hyperbolic Grid

The Hyperbolic Grid fills a disc with a tiling in the style of M. C. Escher's Circle Limit prints. Identical polygons cover the disc, shrinking without end toward its rim, and the whole tiling glides slowly through itself so tiles stream out of the centre and toward the edge.

How it works

This is a map of hyperbolic space, a geometry in which more polygons fit around each corner than a flat floor allows. Squeezed into a disc, every tile is in truth the same size; they only look smaller as they approach the rim, which is infinitely far away. The glide is a true motion of that space, so no tile is ever stretched out of shape. Line widths follow the same rule, so lines thin out toward the edge with the tiles, and a faint rim and glow mark where the plane ends.

Settings

• Sides is the number of sides of each polygon.
• Valence is how many polygons meet at each corner; the grid raises it automatically when a combination would be flat rather than hyperbolic.
• Drift sets how far the tiling glides through itself.
• Section Size draws every Nth ring of polygons as accent lines.
• Cell Size sets the size of the disc.

Use it for

Portals and mystical floors, mathematics and art education, fantasy scenes and abstract brand worlds. Its sister in circles is the Apollonian Grid; the Portal effect suits it well.