• Maple Worksheet from first class: Euclidean Motions
• Maple Worksheet from second class: Rotations, basic looping commands
• Procedures, square tiling
• Partial progress toward the dodecagon tiling in Project 1.6
• Basic Tilings by Hexagons
• Basics about Complex Numbers
• Gaussian Primes
• Squashing a circle
• Squashing a circle: The Movie!!
• Complex Ellipses
• A spiral of squares
• Dividing a square
• Stereographic projection
• More Experiments with Conformal Maps
• A cool Möbius Band in Maple 9
• Beginning Möbius Transformations
• File of procedures for Möbius Transformations
• File of procedures for Möbius maps applied to circles
• Testing circle procedures
• Hyperbolic maps applied to circles
• Two Möbius maps and all their combinations applied to a circle
• Two Möbius maps: the beginning of enumerating all the words
• Two Möbius maps: finding Schottky circles
• Finding symmetric Schottky circles
• Package for enumerating the words in a free group by Breadth-First Search
• Plotting Schottky circles using BFS
• Depth-First Search (DFS) algorithm just producing the words in the correct order.
• DFS algorithm producing the matrices and plotting the Schottky circles.
• DFS algorithm with termination based on the radius of the circle.
• DFSpoints.mws: Plot only limit points.
• twogen.mpl: FILE of procedures for creating general two-generator groups.
• DFStwogen.mws: general two-generator groups.
• DFSarrays.mws: improved DFS procedure.
• File of procedures for Möbius maps applied to circular arcs
• File of procedures for generating circular arc triangles with prescribed interior angles.
• Maple Worksheet demonstrating inversions in the sides of circular arc triangles.

• GSView: PostScript viewing program for Windows: You need GSview and Ghostscript.
• The PostScript Language Reference Manual (7.8 Mbyte)
• First Guide to PostScript by Peter J. Weingartner
• Mathematical Illustrations: A Manual of Geometry and PostScript by William Casselman, University of British Columbia.
• PostScript File for Squares and Triangles
• Golden Rhombi
• Rhombus Subdivision Pattern
• Recursive definition of Penrose Tiling: A first attempt
• Recursive definition of Penrose Tiling: fixed
• Recursive definition of Chair Tiling
• Similarity in the Penrose Tiling, depth 4
• Similarity in the Penrose Tiling, depth 1
• Center of the Similarity

Links on Penrose and other subdivision tilings

• Aperiodic Tilings at mathpages.com
• Tiling Plane and Fancy, by Steve Edwards, including a section on Penrose tiles.
• Pentaplex Ltd.: sells Pentaplexity and Perplexing Poultry
• Penrose Tilings and Toilet Paper! Sir Roger did not care for his tilings cleaning British bottoms (without due compensation).
• Murderous Maths page on Penrose Chickens
• Examples of self-similar tilings: Chairs, Sphinxes
• periodicity and non-recurrent tilings: subdividing a pentagon
• Quasicrystals
• Self-similar tilings arising from projections
• Complex numbers and similarity constants

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Introduction to Dynamical Systems and Fractals

Notes on Euclidean Similarities