Nonperiodic Tiling

Semiperiodic and aperiodic mosaics

• Semiperiodic tiling
  • Polyforms: polyominos, polyiamonds, polyhexes
  • Pentomino, Conway criterion, Solomon W. Golomb
  • Spiral, Voderberg, pinwheel & quaquaversal tilings
  • Branko Grünbaum, Geoffrey C. Shephard
  • Self-tiling, substitution & sphinx tiling, rep-tiles
• Aperiodic tiling
  • Aperiodic tiling, aperiodic prototiles
  • Wang tiling, Hao Wang
  • Ammann-Beenker tiling, Robert Ammann, Raphael Robinson
  • Penrose tiling, Roger Penrose
  • Quasicrystals, Dan Schechtman
  • Einstein problem

Discussion

• Polygons and Polyhedra (World of Mathematics)
• The Tiles of Infinity (Sebastian R. Prange)
• Forbidden Crystal Symmetry in Mathematics and Architecture (Roger Penrose)
• Computer Based Design of Islamic Geometric Patterns (Craig S. Caplan)
• Pattern in Islamic Art (David Wade)
• Digital & Islamic Art

Assignment

Islamic ornament

Arabeske Studio – Islamic Star – Taprats – Taprats (original)

 

Next topic

Specialized tiling  ▸