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On this page you will find some tessellations, surfaces, and other math stuff along with some basic Mathematica code. Loxodrome Sconce - POV-Ray version: 10/7/08; 3ds Max, MaxScript model: 3/15/11
Dodecaplex (120 Cell) - Mathematica 4.2, POV-Ray 3.6.1, 10/21/08
Geodesic Sphere Knots - Mathematica 4.2, POV-Ray 3.6.1, 2/15/11
“Dinosaur Tessellation” - AutoCAD 2000, AutoLisp, Adobe Photoshop 5.0, 12/9/02
Hopf Fibration - Mathematica 4.2, POV-Ray 3.6.1, 8/12/08
Knotted Surface - AutoCAD 2000, POV-Ray 3.6.1, 4/24/07
Knotted Geodesic Sphere Surface - Mathematica 4.2, POV-Ray 3.6.1, 3/3/11
Polyhedrons with Reaction-Diffusion Patterns - new version: C#, POV-Ray 3.6.1, 12/1/11; old version: C++, Mathematica 4.2, 5/24/07
Spherical Cube with Reaction-Diffusion Pattern - C#, POV-Ray 3.6.1, 11/25/11
Knotted Surface with Reaction-Diffusion Pattern - C#, POV-Ray 3.6.1, 12/9/11
Stereographic Projection of a Loxodrome - new version: C++, POV-Ray 3.6.1, 10/1/08; old version: Mathematica 4.2, 7/18/05
Homography of a Logarithmic Spiral - new version: C++, 10/1/08; old version: Mathematica 4.2, 7/18/05
Boy’s Surface (Bryant-Kusner Parametrization) - new version: POV-Ray 3.6.1, 6/20/06 old version: Mathematica 4.2, MathGL3d, POV-Ray 3.6.1, 5/24/05
Spidron - folded paper, POV-Ray 3.6.1, 7/28/10
Dodeca-Spidroball - POV-Ray 3.6.1, 7/29/10
7 Arm Sphidron - POV-Ray 3.6.1, 7/21/10
"Math Rose" - new version: POV-Ray 3.6.1, 6/21/06 old version: Mathematica 4.2, MathGL3d, 3/5/04
Seifert Surfaces - POV-Ray 3.6.1, 9/24/12
Torus with Knotted Hole - POV-Ray 3.6.1, 7/31/12
Dodecahedral Loxodrome - Mathematica 4.2, POV-Ray, 10/28/11
“Free Spirit Tessellation” - AutoCAD 2000, AutoLisp, Adobe Photoshop 5.0, 5/12/03
Maelström Autostereogram - Mathematica 4.2, SISgen 1.58, 10/1/04
Tetration - Mathematica, 10/8/12
Stereographic Projection of a Dodecahedron - POV-Ray, 10/10/08
Kluchikov’s Favorite Isosurface - C++ version: 7/8/09; Mathematica and MathGL3d version: 2/28/05
Belousov-Zhabotinsky (BZ) Reaction - Mathematica 4.2, 5/10/07
Dual of the Geodesic Sphere - calculated in Mathematica 4.2, rendered in POV-Ray 3.6.1, 2/1/11
Knots Within Knots - Mathematica 4.2, POV-Ray 3.6.1, 3/1/11
Moiré Pattern - POV-Ray 3.6.1 version: 4/15/07, Mathematica 4.2 version: 1/29/05
Spherical Canvas versus Reflective Sphere - POV-Ray 3.6.1, 10/17/07
Torus Knots - Mathematica 4.2, MathGL3d, POV-Ray 3.6.1, 10/31/04
Silver Spirals - AutoCAD 2000, POV-Ray 3.6.1, 8/19/02
Silver Noodles - AutoCAD 2000, POV-Ray 3.6.1, 11/30/10
Intersection of 3 Cylinders - POV-Ray 3.6.1, 12/15/08 Loxodrome - POV-Ray 3.6.1, 10/2/08
Golden Ratio Logarithmic Spiral Transformation - Mathematica 4.2, 6/21/04
Complex Map Polar Transformation: f(z) = e - Mathematica 4.2, 6/14/04^{2 p z}
Fisheye Transformation - Mathematica 4.2, 6/15/04 RSA Encryption (Rivest, Shamir and Adleman) - Mathematica 4.2, 11/15/06
Spirographs - MacDraw (vector art), 1992?
Mathematica Typesetting Shortcuts Here is a Mathematica notebook that summarizes some convenient Mathematica typesetting shortcuts. You can type equations quite quickly in Mathematica once you know these shortcuts. I use these shortcuts to type my class notes in Mathematica. Mathematica Links Mathematica - excellent technical computing software, easy to make beautiful plots and play equations as sounds MathGL3d - free Mathematica package for rendering with OpenGL and writing POV-Ray scripts LiveGraphics3D - software for displaying rotatable 3D Mathematica graphics on the internet JavaView - another program similar to LiveGraphics3D Mathematica Information Center - many sample notebooks & packages Mathematicians The Thirty Greatest Mathematicians - interesting biographies by James Dow Allen Leonhard Euler - had a photographic memory, did his greatest work after he went blind, saying "Now I will have less distraction" Carl Gauss - perhaps the greatest mathematician who ever lived, corrected his family finances at the age of 3 Srinivasa Ramanujan - self-taught mathematician who grew up in poverty and baffled leading mathematicians, developed amazing formulas for pi Évariste Galois - proved there is no quintic formula, died in a duel at age 20 over a woman Andrew Wiles - solver of Fermat's Last Theorem John Nash - the movie "A Beautiful Mind" is based on his life Other Math Links Paul Nylander's Page - at the Virtual Art Museum Sphere Eversion - beautiful animation turning a sphere inside-out by Bill Thurston Penrose Tiling - amazing aperiodic tilings discovered by Roger Penrose, here is a Mathematica notebook by E. Arthur Robinson Hyperseeing - electronic publication by The International Society of the Arts, Mathematics, and Architecture Chatin’s Constant - the infamous “incalculable” constant, the probability that a random algorithm halts Fractional Calculus - fractional derivatives Discrete Cosine Transform - how JPEGs are made Strang’s Strange Figures - unexpected patterns in trig functions Wikipedia article on p Gödel's Incompleteness Theorem - famous paper that supposedly defeats all hope of formally proving all truth. I can’t say I understand it, but it’s interesting (and controversial). Chinese Rings - a simple puzzle that can be solved in no less than 18446744073709551616 moves Number Spiral - interesting pattern of prime numbers echochrome - M.C. Escher video game Probability theory paradoxes - Monty Hall problem, Simpson's paradox The Math Book - by Clifford Pickover, includes some of my math artwork Rose windows - beautiful stained glass windows found in Gothic churches Mathematica Art - I especially like the animated GIFs |