Old Math Software
List of obsolete math software. Some in Java, some in Flash, some in Mac OS of 1990s, some Microsoft Windows, etc.
Spivak is a surface plotter by Jacob Siehler. One interesting feature is that users can drag a point inside a box, and the corresponding point on the surface moves dynamically. User can also turn on the drawing of tangent plane, tangent line, geodesic, and principal curvature lines at that point. There is also SpaceCurve program by the author.
download at http://torus.math.uiuc.edu/jms/java/stereop/ Java
stereop by mathematician John M Sullivan. This applet does Stereographic Projection of regular polyhedrons. User can choose any of cube, tetrahedron, octahedron, dodecahedron, icosahedron, and they are centrally projected onto a sphere. This sphere, is then stereo-graphically projected onto a plane. User can rotate the polyhedron, and see its image on the plane change accordingly.
HyperSpace Polytope Slicer
Mark Newbold has written some beautiful polytope visualization Java appletes. One is called HyperSpace Polytope Slicer, which lets you view any of the 6 4D regular polytopes by slice.
Hyperspace Star Polytope Slicer
It is very well-done, and with very detailed explanations. (2003-09,2006-08)
Pedagoguery Software. (2001-01,2006-08) Mac OS Classic Windows
Poly is another interactive 3D program that does polyhedra. This program contains a fairly complete set of regular and semi-regular solids that includes: Platonic, Archemedean, Prism and Antiprisim, Johnson, Catalan, Dypyramids and Deltohedrons. A special feature of the program is showing the solids as nets (graphs) and flat un-wrapped represenations. (the latter is good for making paper models of the solid.) Poly is a shareware. It's available for Mac and Windows.
Polyhedra Stellations Applet
Polyhedra Stellations Applet, by Vladimir Bulatov. “This applet calculates stellations of majority of uniform polyhedra and their duals.” http://bulatov.org/polyhedra/stellation_applet/ Java ()
http://www.peda.com/tess/Welcome.htmlMac OS Classic Windows
Tess is a symmetry-drawing program made by Pedagoguery Software Inc. Available for Mac and Windows.
Escher Web Sketch
Escher Web Sketch. This is a Java program that lets user interactively draw symmetrical patterns. By Wes Hardaker and Gervais Chapuis.
Tyler is a Java applet that draw tilings. It is written by Melinda Green and Don Hatch.
Bob (Penrose tiling)
Bob is a Windows program that does Penrose tilings, by Stephen Collins at http://www.stephencollins.net/Penrose/Default.aspx Windows
Geometry: Plane Tiling Mathematica Package
PlaneTiling is a Mathematica package for tiling and symmetry illustrations. Author is Xah Lee (me). Requires Mathematica to run.
For more programs that does symmetry or tiling related topic, see Wallpaper groups: References and Related Web Sites .
Mac OS Classic
is a plane tiling shareware written by two mathematicians Daniel H Huson and ?.
The program is capable of generating all possible periodic tiling of the plane. By the words of the authors: “… for interactively designing and systematically generating periodic 2-dimensional tilings and patterns, study symmetry and 2-dimensional geometry, if you are a mathematician, enumerate possible 2-dimensional crystal-structures, if you are a crystallographer or chemist, design complex and interesting patterns, if you are a designer, or explore a whole new world of fascinating periodic structures, if you are, well, just interested.” This program is a bit mathematical, but can be fun for layperson. It is a rare tool for crystallographer and mathematicians. URL:
(Note: This program is from 1995 era. The software downloaded from the ftp site is missing data files, making the software not usable. I don't have a copy of it.)
HyperDimension Ishihama Yoshiaki has written several interesting programs. Many of them are related to high dimensions, including a 4 and 5 dimensional Rubic cube simulators. His programs are small and original, but the interface is very crude. Check out his webpage for more.
Source www.asahi-net.or.jp. Ishihama Yoshiaki's software are usually raw and unpolished. (2002-07) Mac OS Classic Java
Mac OS Classic
HyperSpace 2.0 (1990) is another higher-dimensional polytope viewer, by Paul Bruke. It does not let you drag and spin, but offers both multiple slice view and projection view on about 4 regular polyhedrons.
Hyperbolic Tesselations Applet draws hyperbolic tilings. Superb! By Don Hatch.
MoebApplet, by Paul Murray. This Java applet does real-time interactive Mobius transformation. If you are studying Mobius Transformation, this is the best applet for it. You can drag the fixed points, the poles, and a few other critical points in the plane and see the image change as you move.
Interactive plane geometry software
Interactive plane geometry software were made popular first by Geometer's Sketchpad at least back to 1994. It is a wonderful tool made possible by technology. Such program allows one to construct plane geometry drawings dynamically, much in the way of Greek's “Ruler and Compass”. For example, draw a triangle with lines bisecting the 3 angles. They intersect in a point called the incenter of the triangle. (which is also the center of the largest possible circle inside.) Now, you can drag the corners of your triangle to change its shape, and all your drawings change accordingly. Because of such dynamic power, a few theories on plane geometry have been found because of such software.
In the 1990s, there's only Geometer's Sketchpad and Cabri Geometry. In late 1990 came Cinderella, written in Java. But since about post 2000, there's a explosion of interactive geometry software. As of 2007, there are more than ten of them (counting only quality ones), many of them are free. They are all similar. They are all of high quality. Almost all of them can be saved as Java appletes so that it can be placed on the web for students to use without needing extra software. Their features differ slightly. Several of them are FreeSoftware. The following is a short commentary of the ones i've actually used (except otherwise stated).
The Geometer's Sketchpad, created by Nicholas Jackiw. This is the one that started dynamic geometry software in the early 1990s, and is still excellent. macOS Mac OS Classic Windows
CaR (plane geometry)
http://www.asahi-net.or.jp/~hq8y-ishm/ Mac OS Classic macOS
Simulations by Ishihama Yoshiaki. This program does lots of artificial life simulations. The program is a bit of crude. It works like a screensaver, where you just watch the interactions on the screen, and you can adjust some parameters. The program has simulations like flocks of bird, fish school, worms, swarms, and also simulate centipedes showing its gaits, and then spiders, ants, etc. It's basically a collection of simulations that satisfies the programer's curiosities himself. Not a full-fledged program nor polished, but very inspiring.
Boid by Craig Reynolds, is one of the original boid machinenary. Basically, it is computer simulation of the bahavior of flock of birds or school of fishes. The gist is that each move according to the behavior of their nearest neighbors. Fascinating.
Cellebration (cellular automata)
Cellebration by Mirek Wojtowicz plays ~12 types of Cellular Automata. This Java applet plays many types of CAs. The complete source code and binary are available for download.
modernca (cellular automata)
The site features CA gallery using Java Appletes. By George Maydwell. Java
2002-05: many good cellular java appletes programs written by computer science students on a CA course. Includig cellular automata on triangular and hexagonal grids, as well as some regular tilings. Professor is Carter Bays.
Tiled CA (cellular automata)
Puzzler is a Windows program by Noel Dilabough. Puzzler plays all types of magic polyhedrons. Puzzler plays some 20 non-trivial variations of magic polyhedrons, including the five platonic solids with different cuts. The program is great, unique, but the interface is very bad. Extremely frustrating to use. Puzzler is a shareware.
http://www.superliminal.com/cube/cube.htm. () Windows Linux Java
MagicCube4D by Don Hatch and Melinda Green. It plays 4-dimensional Magic Cube. It also maintains record of the world's first solvers and a solution database. The source code is also available.
4DRubikCubehttp://www.asahi-net.or.jp/%7Ehq8y-ishm/hyper.html Mac OS Classic Windows Java
4DRubikCube by Ishihama Yoshiaki is a 2x2x2x2 magic cube simulator.
http://kevingong.com/Polyominoes/index.html macOS Mac OS Classic Java WindowsPolyominoes is a polyominoes fitting game. Written by Kevin L Gong. In this program, you try to fit a set of polyominoes (connected squares) into a given shape. In another mode, two players take turns fitting polyominoes into a give shape. The first without a fitting piece losses. It's almost impossible to beat the computer. Mac, Windows and Java.
Pentominos Puzzle Solver
http://math.hws.edu/xJava/PentominosSolver/ (2018-04-07) Java
Pentominos Puzzle Solver A pentominos solver, by David Eck.
Mac OS Classic
★ Tangram (v 4.1, 1999-07. ) Tangram is a popular tiling puzzle that's probably originated from China. The goal is to arrange a set of seven tiles to match a given shape. This software's interface is beautiful and well-designed. Author is S. T. Han (firstname.lastname@example.org).
.Mac OS Classic
★ Poly-Peg 1.09 by S T Han. This puzzle is sometimes known as peg solitaire. You remove pieces on a board by jumping other pieces over it. The goal is to leave only one piece on the board. PolyPeg lets you edit your own shape of square or hexagonal board and set whether diagonal jump are allowed in square board. It also include a auto solve feature.
Pegged is a small mac program that plays Peg Solitare. It offers the traditional cross shaped board, but with 7 arrangement of end games. Written by Cary Torkelson in 1991, but still works great under Mac OS X Classic 2003.
★ Poly-Off 1.09 is another excellent shareware by S. T. Han. The game Poly-Off can be thought of as one type of cellular automata. In a square or hexagonal grid, you switch on or off a cell that will affect neighbor cells. The goal is to switch off all cells. I had lots of fun with this program.
Mac OS Classic
★ Poly-Dol v.1.01 by S. T. Han. The puzzle in this program is similar to a commercial program named Cogito. You shift pieces on a board until all the pieces are in certain order. You can only shift pieces in certain row, column, or array of the board. There are dozen boards to choose for play and you can make your own board shapes. I find this program to be much fun. For Mac and Windows.
Mac OS Classic
★ Poly-Tile v.1.04 by S. T. Han. This puzzel is similar to a commercial program named Tesserae, published by In-Line designs Inc. In this puzzle, Tiles of different design are layed over a board. You remove them one at a time by jumping (flipping) adjacent tiles of the same design. The goal is to leave only one tile on the board. I find this game too difficult. It's also hard to analyze because the random initial placement and designs. Like Poly-Peg and Poly-Dol, you can customize your board when you got bored with the given configurations.
2005-10: Sokoban (倉庫番=warehouse keeper) is a classic game invented by Hiroyuki Imabayashi in 1982. It is a puzzle where the player pushes boxes around a maze to designated locations.
★ MYHOUSE is a clever and fun logic puzzle, by M Aono. It is a variation of the classic Sokoban. Your goal is to move a bunch of shrimps home. The shrimps move in sync. When one bump into wall, it doesn't move but the rest moves. The red blocks are fire and if one shrimps runs into it you die. Your goal is to align all shrimps in such way to move them home.
Klotski is a classic sliding block puzzle. Your goal is to slide the red block all the way to the right side center. Yes, it can be done. This puzzle is dicussed in Scientific American, March 1995 (Volume 272 Number 3 Pages 108-110), Mathematical Recreations by Ian Steward. A beautiful wooden set of this puzzle has been marketed by various companies.
Loyd's Lunacy is another block-sliding logic puzzle. The goal is to slide the large square from upper right corner to upper left. Author is Chip Moody. Written in 1990 but still works great under Mac OS X Classic in 2003. This program has a very funny “About” dialogue.
Dirty Dozen is a block-sliding logic puzzle. Writen by Nick Triantos in 1993 but still works under Mac OS X Classic in 2003.
by Viktor Massalogin. KriviznaPlus draws the Stereographic Projection from 3D to plane. KriDva draws the stereographic projection of S^3 sphere (x^2+y^2+z^2+z^2==r^2) to the 3D space. These programs are extremely fun and beautiful. I hope the author adds more explanations on the math. As of 2004, he added another version CPace.
[see Stereographic Projection]
Space Jewels is a Java game, where you drive a spaceship in hyperbolic space to collect jewels. Author is Matthew Cook (born 1970). Matthew Cook
He has a write up http://www.paradise.caltech.edu/%7Ecook/Workshop/Math/HyperbolicLand.html
http://www.jwz.org/xscreensaver/screenshots/ Linux macOS Windows
xscreensaver by Jamie Zawinski is a screesaver for unix's X-Windows. A huge collection.
http://www.efn.org/~jcburg/software.shtml Mac OS Classic (2003-10)
Koch Toy by Jim Burgess is another excellent simple program. It draws simple fractal curves like that of Koch snowflake. User drag points on a line and immediately see its effects after n iterations. The number of kinks can be adjusted by dragging the nodes. Clicking on a arrow button increase or decrease recursion depth.
Vectal draws simple fractal curves like that of Koch snowflake. User drag points on a line and immediately see its effects after n iterations. One feature of Vectal not in the mac Koch Toy is that user can change the sided-ness of the fractal on each line.
Fracture, a fractal-generating screensaver, by Ben Haller.
Ben is also the author of the famous AfterDark screensaver module Satori, Rose, Lunatic Fringe. (Satori is the mesmeric color changing pattern. Rose is the dotted pattern of the math rose curve).
[see Rose Curve]
FlowFazer by David Levine.
StdMap. Standard Maps displays the dynamics of several area preserving mappings. It will also find periodic orbits, cantori, and stable and unstable manifolds of any (symmetric) periodic orbit.
The program is written by mathematician J D Meiss.
1DMap is another program by mathematician J D Meiss. It plots orbit maps of various equations, including: logistic, cosine, cubic, exp, tangent, tent, circle. For each, one can plot the correspondig cobweb, bifurcation diagram, and other statstical diagrams. The program is intuitive, but there is no documentation or tutorial, so the reader must already be familiar with the mathematics. Some textbooks on 1D dynamic systems are suggested on his website.
by mathematician J D Meiss.
Cycle Explorer is a simple program that draws orbit maps of the equation f[x]:=x^2+c. Author is Jim Burgess.
Mac OS Classic (2003-10)
ABC Map “abc, iterate a 3D volume preserving system”. It plots orbit maps of what seems various 3D formulas of significance. I don't quite understand the math here. However, this program is wonderful in that it is like a screensaver with mesmeric images. Dots appears in a 3D box, and these dots fluctuate seemingly ramdomly that forms very distinct patterns. It's like watching statics on TV, but the statics form unpredicable patterns constantly. One can rotate the box. It is a fantastic program even if one knows nothing about the math. The equation it plots has these names: Froeshle, Arnold, ABC, Integrable, Adriana, and others. I hope the author writes a minimum amount of tutorial to benefit the masses.
by mathematician J D Meiss
http://amath.colorado.edu/faculty/jdm/abc.html macOS (2003-10)
IFS Another program by mathematician J D Meiss. This program does the Iterated Function Systems. It comes with a tutorial on IFS. Nice. After reading the one-page tutorial, I understand that IFS is as follows: we have n mappings of the plane. For each iteration, one of them is chosen by a given probability function. So, we start with some points or line in a plane, then apply the functions in each iteration, and plot the transformed points or line accumulatively.
http://amath.colorado.edu/faculty/jdm/ifs.html Mac OS Classic (2003-10, 2012)
Icon Maker is a simple program that draws orbit maps of the equation
f[z]:=z*(λ + α*z*conjugate[z]+β*Real[z^n]+ω*i)+γ*Conjugate[z]^(n-1)
and other variants. The program is based on ideas in the book Symmetry in Chaos by M Field, M Golubitsky, 1992. This is a wonderful, easy to use, and beautiful program. Author is Jim Burgess.
Mac OS Classic (2003-10)
Bulli Python by Andrew Cooke.
This program generates Parquet deformations (gradual shifting of patterns). You need to be a python programer in order to install and use this program.