Visual Mathematics

New Stuff

• Necker Tiler:
  Web application for making patterns from projections polyhedral surfaces built from rectangles in ℝ³. For examples, see the gallery.
• FlatSurf:
  Software for working with translation surfaces using SageMath.
• Driving on a Truchet Tiling:
  Go on a roadtrip through a quasiperiodic tiling.
• Truchet dynamics:
  This is a java program which allows the user to investigate quasi-periodic patterns of Truchet tiles.
• Web background generator:
  Create periodic backgrounds using area preserving dynamics on a torus.
• Gallery:
  View a gallery of user generated content.

Billiards

• McBilliards II:
  A program for investigating periodic billiard paths in convex polygons.
• McBilliards:
  A java based program that investigates periodic billiard paths in triangles. This program is joint work with Rich Schwartz.
• Finding infinitely many billiard paths in irrational triangles:
  A brief argument can be used to show some irrational triangles have infinitely many periodic billiard paths.
• Some Cylinder Decompositions of a Veech Surface:
  I generated some pictures of these when I was investigating the (Pi/3, Pi/12, *) triangle.

Other stuff

• Deform Real Projective Structures Applet:
  Start with a standard real projective structure on an genus 2 surface and deform it.
• Applet Demonstrating the dynamics of some Area Preserving Maps
  It can be used to create some interesting tiled web-page backgrounds!
  Original Applet or Web Background Generator
• A Schottky Group applet
  View the domain of discontinuity of the group of reflections in a chain of tangent circles.
• Langton's Ant
  • Description --- Original Applet --- Ant with more freedom
  • Langton's Ant Paired with a friend:
    
    Slide Shows: Fractal Constructions --- Triangle Formations --- Crystals and Spirals --- Other Neat Images
    Applets: Reflected --- Rotated --- Diagonal Reflection
  • Langton's Ant Running on a deformed grid (a java applet)
    
    The set of squares that "Ant 6" has visited after a while begins to look much like a cardioid. Suprisingly, this behavior persists under a large number of deformations of the grid of squares near the origin. This applet demonstrates this phenomenon.
  • Old Applet --- Old Hexagonal Grid Applet
• Some Animated Fractals!
• Robinson Tiling Applet
  Play with a bunch of tiles that only tile the plane non-periodically.
• A description of Pappus' Theorem and Steiner's Theorem
  Later I published a paper on the subject.
• Play with Trace Zero Projective Transformations of the Plane
  (No documentation)