Software and Animations

I've included here pointers to downloadable software, for interactive or animated geometry. But I'm not generally including web applets or other code intended for use while browsing, because there's just so much of it and it's an integral part of many of the pages I link to rather than drawing attention to itself as software.

• Algorithmic mathematical art, Xah Lee.

• Cinderella multiplatform Java system for compass-and-straightedge construction, dynamic geometry demonstrations and automatic theorem proving. Ulli Kortenkamp and Jürgen Richter-Gebert, ETH Zurich.

• Circle packing and discrete complex analysis. Research by Ken Stephenson including pictures, a bibliography, and downloadable circle packing software.

• Cognitive Engineering Lab, Java applets for exploring tilings, symmetry, polyhedra, and four-dimensional polytopes.

• Dreamscope screen-saver module makes patterns with various Kaleidoscopic symmetries.

• DUST software for visualization of Voronoi diagrams, Delaunay triangulations, minimum spanning trees, and matchings, U. Köln.

• Gavrog, a Java package for visualizing 2d and 3d ornamental patterns with high degrees of symmetry.

• Geometria Java-based software for constructing and measuring polyhedra by transforming and slicing predefined starting blocks.

• Geometric Java applets by Fergus C. Murray produce screensaver-like interactive images. See also his noninteractive mathematical animations and stills.

• Geometry turned on -- making geometry dynamic. A book on the use of interactive software in teaching.

• GeoProof interactive geometry software including automated theorem proving methods.

• Great math programs. Xah Lee reviews mathematical software, focusing on educational Macintosh applications. Includes sections on geometric visualization, fractals, cellular automata, and geometric puzzles.

• HypArr, software for modeling and visualizing convex polyhedra and plane arrangements, now seems to be incorporated as a module in a larger Matlab library for multi-parametric analysis.

• Hyperbolic Geometry using Cabri.

• Hyperdimensional Java. Several web applets illustrating high-dimensional concepts, by Ishihama Yoshiaki.

• HyperGami program for unfolding polyhedra, also described in this article from the American Scientist.

• Information on Pentomino Puzzles and Information on Polyominoes, from F. Ruskey's Combinatorial Object Server.

• Interactive Delaunay triangulation and Voronoi diagrams:
  VoroGlide, Icking, Klein, Köllner, Ma, Hagen.
  D. Watson, CSIRO, Australia.
  Baker et al., Brown U.
  Paul Chew, Cornell U.
  

• Java applets on mathematics, Walter Fendt.

• Java gallery of geometric algorithms, Z. Zhao, Ohio State U.

• Java quadric surface raytracer, P. Flavin.

• Jenn open-source software for visualizing Cayley graphs of Coxeter groups as symmetric 4-dimensional polytopes.

• Kaleidotile software for visualizing tilings of the sphere, Euclidean plane, and hyperbolic plane.

• Kali, software for making symmetrical drawings based on any of the 17 plane tiling groups.

• kD-tree demo. Java applet by Jacob Marner.

• LightSource sacred geometry software.

• Line designs for the computer. Jill Britton brings to the web material from John Millington's 1989 book on geometric patterns formed by stitching yarn through cardboard. The Java simulation of a Spectrum computer running Basic programs is a little (ok a lot) clunky, and froze Mozilla when I tried it, but there's also plenty of interesting static content.

• Logical art and the art of logic, pentomino art, philosophy, and DOS software, G. Albrecht-Buehler.

• Manipula Math with Java. Interactive applets to help students grasp the meaning of mathematical ideas.

• MicroGeometry volume and surface area calculator for the Palm.

• Minesweeper on Archimedean polyhedra, Robert Webb.

• More hyperbolic tilings and software for creating them, J. Mount.

• Non-Euclidean games implemented in Shockwave by students in an advanced high school geometry class: projective-plane asteroids, hyperbolic double-torus minesweeper, and cubical fruitarian snake.

• Non-Euclidean geometry with LOGO. A project at Cardiff, Wales, for using the LOGO programming language to help mathematics students visualise non-Euclidean geometry.

• Oops image warper, based on three simple geometric transformations.

• Packing results, D. Boll. C code for finding dense packings of circles in circles, circles in squares, and spheres in spheres.

• Peek, software for visualizing high-dimensional polytopes.

• Perron Number Tiling Systems. Mathematica software for computing fractals that tile the plane from Perron numbers.

• Points on a sphere. Paul Bourke describes a simple random-start hill-climbing heuristic for spreading points evenly on a sphere, with pretty pictures and C source.

• Poly, Windows/Mac shareware for exploring various classes of polyhedra including Platonic solids, Archimedean solids, Johnson solids, etc. Includes perspective views, Shlegel diagrams, and unfolded nets.

• Polygon Puzzle open source polyomino and polyform placement solitaire game.

• Polyomino applet, Wil Laan.

• Polyominoes 7.0 Macintosh shareware.

• Polytopia CD-ROMs on tessellations, polyhedra, honycombs, and polytopes.

• Postscript geometry. Bill Casselman uses postscript to motivate a course in Euclidean geometry. See also his Coxeter group graph paper, and Ed Rosten's postscript doodles. Beware, however, that postscript can not really represent such basic geometric primitives as circles, instead approximating them by splines.

• Prolog soma-cube puzzle program.

• ProtoZone interactive shockwave museum exhibits for exploring geometric concepts such as symmetry, tiling, and wallpaper groups.

• Quicktime VR and mathematical visualization.

• Realizing a Delaunay triangulation. Many authors have written Java code for computing Delaunay triangulations of points. But Tim Lambert's applet does the reverse: give it a triangulation, and it finds points for which that triangulation is Delaunay.

• Reconstruction of a closed curve from its elliptic Fourier descriptor. The ancient epicycle theory of planetary motion, animated in Java.

• Rectangular cartograms: the game. Change the shape of rectangles (without changing their area) and group them into larger rectangular and L-shaped units to fit them into a given frame. Bettina Speckmann, TUE. Requires a browser with support for Java SE 6.

• Vittoria Rezzonico's Java applets. Hypercube and polyhedron visualization, and circle inversion patterns. Requires both Java and JavaScript.

• Sensitivity analysis for traveling salesmen, C. Jones, U. Washington. Still a good title, and now the geometry has been made more entertaining with Java and VRML.

• SingSurf software for calculating singular algebraic curves and surfaces, R. Morris.

• SnapPea, powerful software for computing geometric properties of knot complements and other 3-manifolds.

• Soma cube applet.

• SpaceBric building blocks and Windows software based on a tiling of 3d space by congruent tetrahedra.

• Sphere packing and kissing numbers. How should one arrange circles or spheres so that they fill space as densely as possible? What is the maximum number of spheres that can simultanously touch another sphere?

• Spiral generator, web form for creating bitmap images of colored logarithmic spirals.

  

• sqfig and sqtile, software by Eric Laroche for generating polyominoes and polyomino tilings.

• Stella and Stella4d, Windows software for visualizing regular and semi-regular polyhedra and their stellations in three and four dimensions, morphing them into each other, drawing unfolded nets for making paper models, and exporting polyhedra to various 3d design packages.

• Stellations of the dodecahedron stereoscopically animated in Java by Mark Newbold.

• Wilson Stothers' Cabri pages. Geometric animations teaching projective conics, hyperbolic geometry, and the Klein view of geometry as symmetry.

• SymmeToy, windows shareware for creating paint patterns, symmetry roses, tessellated art and symmetrically decorated 3D polyhedron models.

• Taprats Java software for generating symmetric Islamic-style star patterns.

• 3d-XplorMath Macintosh software for visualizing curves, surfaces, polyhedra, conformal maps, and other planar and three-dimensional mathematical objects.

• TileDreams Windows software for creating symmetric patterns with rhombi.

• The tiling puzzle games of OOG. Windows and Java software for tangrams, polyominoes, and polyhexes.

• Touch-3d, commercial software for unfolding 3d models into flat printouts, to be folded back up again for quick prototyping and mock-ups.

• Ukrainian Easter Egg. This zonohedron, computed by a Mathematica notebook I wrote, provides a lower bound for the complexity of the set of centroids of points with approximate weights.

  

• UMass Gang library of knots, surfaces, surface deformation movies, and minimal surface meshing software.

• Uniform polyhedra in POV-ray format, by Russell Towle.

  

• Virtual Image, makers of CD-ROMS of ray-traced mathematical animation.

• Visualizations of 4d hypercube (Java applet).

• vZome zometool design software for OS X and Windows. (Warning, web site may be down on off-hours.)

• Wallpaper patterns, R. Morris. Kaleidoscope-like Java applet for making and transforming symmetric tilings out of uploaded photos.

• Wingeom, freeware Windows geometric construction software.

• WWW spirograph. Fill in a form to specify radii, and generate pictures by rolling one circle around another. For more pictures of cycloids, nephroids, trochoids, and related spirograph shapes, see David Joyce's Little Gallery of Roulettes. Anu Garg has implemented spirographs in Java.

• Yantram sacred art toolbox. Software for creating various kinds of symmetric fractal mandala.

• yukiToy. Shockwave plugin software for pushing around a few reddish spheres in your browser window. But what exactly is the point? (They're spheres, they don't have one, I guess.)