In simple terms, it is taking a pattern, repeating it in every direction as if it were on a beach ball, giving it a 3D spherical effect on a flat 2D surface. The pattern becomes smaller, curved and skewed as it expands outward until it turns into a circular outline.
The math behind all this is best left to these wonderful people and their web sites…
- Sculptural Forms from Hyperbolic Tessellations
- David Joyce, Department of Mathematics and Computer Science at Clark University
- Math and Art of MC Escher, St. Louis University
- Don Hatch, Hyperbolic Planar Tessellations
- Dmitry Brant, Hyperbolic Tessellations
- Douglas Dunham, Transformation of Hyperbolic Escher Patterns
- Jos Leys, Mathematical Imagery Blog: Hyperbolic Chamber
- David Eppstein, The Geometry Junkard
The order of this list reflects how I found them via Google versus any judgment regarding their order of expertise. – Maureen
- Cool Math Lessons – What are Tessellations?
- Interactive: Tessellate! (cool app)
- Math Forum: What is a Tessellation?
- How to Make an Escher-esque Tessellation (video)
- Making an Escher-like Tessellation w/brief Escher History (video)
- Anatomy of an Escher Flying Horse (video)
- How to make a Tessellation (video)
- Simple Bird Tessellation (video)
- Hexagon Tessellation (video)