Symmetry and Ornament

Periodic tiling and interlocking mosaics

• Ornament theory
  • Ornament, history of decoration
  • From quintic function to symmetry, Niels Henrik Abel, Évariste Galois
  • Group theory, symmetry groups
  • Euclidean plane isometry, rotation, translation, reflection, glide reflection
• Symmetry of rotation
  • Reflection and rotational symmetries, chirality, helix
  • Rose window, kaleidoscope, mandala, snowflakes, floral symmetry
  • Cyclic and dihedral groups
• Symmetry of translation
  • Translational symmetry
  • Frieze groups
• Periodic tiling of the plane
  • Tessellation, Euclidean tilings
  • Wallpaper groups, Dirichlet domain
  • Regular tiling, uniform tiling, Archimedean tiling, Pythagorean tiling
  • Evgraf Fedorov, Arthur Moritz Schönflies, George Pólya
  • Regular division of the plane, M. C. Escher
  • Islamic ornament and geometric patterns
  • Arabesque, zellij, girih, muqarnas

Discussion

• Transformations and Symmetry (World of Mathematics)
• Tessellation Patterns - From Mathematics to Art
• Math and the Art of M. C. Escher (Anneke Bart & Bryan Clair)
• Symmetry, Reality’s Riddle (Marcus du Sautoy)
• Finding Moonshine: A Mathematician's Journey Through Symmetry (Marcus du Sautoy)
• The Free Book of Symmetry Notation (Jabra Ghneim)
• Algorithmic ornament. Mostly. (Regolo Bizzi)

Assignment

Escher tiling

EscherSketch – Escher Web Sketch – Escherizace – Fractal Backgrounds – Kaleidomania – Kaleidoskop – KaleidoTile – MosaicGen – Mospaint – Ornament – Random Quilts – Tess – Tessellation Kit – TesselManiac! – Tilemaker

 

Next topic

Nonperiodic tiling  ▸