Doug Dunham has several papers on our site reporting his studies of tiling in hyperbolic space.

He has several things on offer; how that space changes the rules we know from ordinary space; how to adapt artistically inspired tilings based on these rules; and how to diagram the results.

The last of these (in the context of the others) is what is of interest to us. Dunham follows the usual convention of drawing a disk that represents the horizon of the space, and then has developed a way to diagram how regular tiles distort and shrink as they approach this horizon. 

The Relationship to Kutachi

We have several metaphors that use both a notion of space or distance and a visible limit at infinity. For example, we need to display an ontology graph. Many of these will have effectively infinite leaves, yet we need to be able to show something of the structure of the thing, especially as it approaches infinity.

Links

Artistic Patterns with Hyperbolic Symmetry. Doug Dunham. [Symmetry of Structure] 1989.

The Kutachi essay on Lightning. (not online yet)

The Kutachi essay on Quantum Clouds. (not online yet)

The Kutachi essay on Semantic Distance. (not online yet)