1. Mathartfun.com - Where Math, Art Fun Come Together! Books, puzzles, posters and art gallery related to tessellations, polyhedra, fractals, anamorphic art, and M. C. Escher. Arizona, USA. Also order http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Index Page With Books Window Books related to math and art. Escher, tessellations, polyhedra, fractals and more. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Catalogs For Kits Other Educational Products , Free Lewis Part of the extensive searchable archives of the Homeschool Mailing List, full of educational resources for *all* educators. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. MavicaNET - Polyhedra Browse topics including tessellations, polyhedra, fractals, anamorphic art, kaleidoscopes, M. C. Escher and Origami. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Efg's Fractals And Chaos Von Koch Curve Lab Report Koch's Flakes in "Fractals Polyhedra, Flakes Ltrees" www.people.nnov.ru/fractal/VRML/3dLsys/. .. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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7. The Geometry Junkyard Fractals S ndor Kabai's mathematical graphics, primarily polyhedra and 3d fractals. Labyrinth tiling. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. The Math Forum - Math Library - Polyhedra amusement park of mathematics" for exploring math functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. 3D Fractals This is an extension of my wireframe applet. It generates 3dimensional 'fractals' by superimposing polyhedra upon themselves recursively. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Math Sites Topics include polyhedra, fractals, probability and statistics, etc. 7 12 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Fractals Based On Regular Polygons And Polyhedra Fractals based on regular polygons and polyhedra. Source, Scientific visualizationof physical phenomena table of contents. Pages 299 314 http://portal.acm.org/citation.cfm?id=139834.139887

12. Help Contents / Examples / Polyhedra-fractals (3d Fractal) polyhedrafractals (3d fractal). This example draws three polyhedra based ontheir face-to-face angle and their net. On every face another smaller tetraeder http://www.physik.uni-augsburg.de/~micheler/Elica-5.0-HTML-help-0.3/help/polyhed

Polyhedra-fractals (3d fractal) Help Contents Examples Polyhedra-fractals (3d fractal) Pascal-Assignment (simple) Pythagoras (advanced) Polyhedra-fractals (3d fractal) This example draws three polyhedra based on their face-to-face angle and their net. On every face another smaller tetraeder is placed, so that a 3d fractal grows, similar to a Koch-snowflake curve. run graphix run run ... zoomRotate ; allow zoom-rotating during the construction to norm :p output sqrt (:p.x*:p.x+:p.y*:p.y+:p.z*:p.z) end ; make onbeforedraw fog fog "true 100 1 0.1 black make onbeforedraw clearcolor ... make "maxs 32 ; maximal side length make "mins 16 ; minimal side length make "i maxs*( sqrt (2/3)) ; i = inner height of tetraeder make "alpha arctan sqrt 8 ; 72.5° inner tetraeder angle make "poly [ [:points : color run bf polygon ; this is how multiple inheritance works in Elica! local "mode "width "smooth ;"shininess "material.specularity make "mode 2 make "width 3 make "smooth "true ; make "pattern [xo ox] make color .#1 128 ; alpha-level ; range : 0..255 ; 255 means solid, ; 128 half transparent, ; completely transparent. ;

13. Modular Origami - Models Folded By Michaà ‚ Kosmulski Images of modular origami models folded by Michaà ‚ Kosmulski. Model categories include fractals and IFS, interesting mathematical objects, polyhedra and balls, spiked balls and stars. http://hektor.umcs.lublin.pl/~mikosmul/origami/index.html

Modular Origami On these pages you can find images of some models I have folded. Instructions for most modules used for them can be found on the Web and links to module authors' pages are given where appropriate. Some of the arrangements are classical, well-known models, while others are my own inventions. Fractals Balls and Polyhedra Intersecting planes Spiky balls and stellated polyhedra ... Origami links Michaà ‚ Kosmulski Home Minerals, Fossils, Meteorites setMenuState('minfosmet_menu'); My Collection Images of Specimens setMenuState('spec_minfosmet_menu'); Minerals Fossils Meteorites Rocks ... Modular Origami setMenuState('origami_menu'); Introduction Fractals Planars Spiky Balls ... Computing setMenuState('comp_menu'); Software projects setMenuState('soft_comp_menu'); Dark Garden Zeta KmdrProperties Kuote (KDE Fish Applet) ... Published Articles setMenuState('articles_comp_menu'); Custom keyboard layouts OpenOffice.org macros Linux and Unicode A Kommander Crash Course setMenuState('tips_comp_menu'); Introduction Mozilla Thunderbird Audio recording Setting CD-ROM speed ... Juliusz Sà ‚owacki setMenuState('slowacki_menu'); Biography Links Marian Smoluchowski setMenuState('smoluchowski_menu');

14. Help Contents / ZoomRotate mouse button pressed, rotate with the left mouse button pressed, while andafter the drawings take place. Example see polyhedrafractals (3d fractal) ! http://www.physik.uni-augsburg.de/~micheler/Elica-5.0-HTML-help-0.3/help/zoomrot

ZoomRotate Help Contents ZoomRotate picbutton ZoomRotate With this little library you can zoom and rotate any 3D drawings with your mouse. Usage: place the line run zoomRotate before your 3D drawings, but after loading " graphix and then zoom with the right mouse button pressed, rotate with the left mouse button pressed, while and after the drawings take place. Example: see Polyhedra-fractals (3d fractal) This library is under construction. (AM) run io local "mouse "radius "eye "focus "upwards "running "theta "phi "phiIncrement make "radius 70 make "eye vector radius make "focus vector make "upwards vector 1 to ButtonEnd make zoomRotate .onmousemove ; KeyboardOff ; WindowDelete "mywindow make "running "false end to ButtonReset make "theta 17 make "phi 10 make "phiIncrement 1 mouse.up make "rotateStartPos :mouse.pos mouse.rotate end to updateView ; StaticUpdate "staticzoomRotate.theta Se "theta: form :theta 4 ; StaticUpdate "staticzoomRotate.phi Se "phi: form :phi 4 make "rotateStartPos :mouse.pos ( make "eye ( vector :radius*( cos :theta)*( sin :phi) :radius*( sin :theta) :radius*( cos :theta)*( cos :phi) ) ) lookat :eye :focus :upwards ; setTurtle -3 ; some light

15. Mathartfun.com - Where Math, Art & Fun Come Together! Books, puzzles, posters and art gallery related to tessellations, polyhedra, fractals, anamorphic art, and M. C. Escher. Arizona, USA. Also order tollfree. http://mathartfun.com/shopsite_sc/store/html/index.html

16. The Geometry Junkyard: Fractals Felix Golubov makes random triangulated polyhedra in Java by perturbing the Sándor Kabai s mathematical graphics, primarily polyhedra and 3d fractals. http://www.ics.uci.edu/~eppstein/junkyard/fractal.html

Fractals Allegria fractal and mathematically inspired jewelry. Apollonian Gasket , a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles. From MathWorld. Area of the Mandelbrot set . One can upper bound this area by filling the area around the set by disks, or lower bound it by counting pixels; strangely, Stan Isaacs notes, these two methods do not seem to give the same answer. Balanced ternary reptiles Cantor's hourglass reptile spiral reptile stretchtiles ... trisection of India , the three Bodhi problem , and other Fractal tilings by R. W. Gosper Circle fractal based on repeated placement of two equal tangent circles within each circle of the figure. One could also get something like this by inversion, starting with three mutually tangent circles, but then the circles at each level of the recursion wouldn't all stay the same size as each other. The Curlicue Fractal , Fergus C. Murray. The Dynamic Systems and Technology Project at Boston Univ. offers several Java applets and animations of fractals and iterated function systems. Expansions geometric pattern creation techniques by John S. Stokes III.

17. The Geometry Junkyard: Polyhedra And Polytopes Sándor Kabai s mathematical graphics, primarily polyhedra and 3d fractals.KeplerPoinsot Solids, concave polyhedra with star-shaped faces. http://www.ics.uci.edu/~eppstein/junkyard/polytope.html

Polyhedra and Polytopes This page includes pointers on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes). Other pages of the junkyard collect related information on triangles, tetrahedra, and simplices cubes and hypercubes polyhedral models , and symmetry of regular polytopes Adventures among the toroids . Reference to a book on polyhedral tori by B. M. Stewart. Bob Allanson's Polyhedra Page . Nice animated-GIF line art of the Platonic solids, Archimedean solids, and Archimedean duals. Almost research-related maths pictures . A. Kepert approximates superellipsoids by polyhedra. Archimedean polyhedra , Miroslav Vicher. Archimedean solids: John Conway describes some interesting maps among the Archimedean polytopes . Eric Weisstein lists properties and pictures of the Archimedean solids Rolf Asmund's polyhedra page Associahedron and Permutahedron . The associahedron represents the set of triangulations of a hexagon, with edges representing flips; the permutahedron represents the set of permutations of four objects, with edges representing swaps. This strangely asymmetric view of the associahedron (as an animated gif) shows that it has some kind of geometric relation with the permutahedron: it can be formed by cutting the permutahedron on two planes. A more symmetric view is below. See also a more detailed description of the associahedron , and Jean-Louis Loday's paper on associahedron coordinates David Bailey's world of tesselations . Primarily consists of Escher-like drawings but also includes an interesting section about Kepler's work on polyhedra.

18. Fractals Index, Geometry, Formats, Curves, Surfaces, polyhedra, fractals, Chaos, Projection,Stereographics, Rendering, Radiance, PovRay, OpenGL, Modelling, Terrain http://astronomy.swin.edu.au/~pbourke/fractals/

F r a c t a l s , C h a o s Index Papers Geometry Curves Surfaces Fractals, Chaos Projection Stereographics Raytracing OpenGL Modelling Colour Textures Data Formats Fun, puzzles Other Old stuff POVRay Fractal Raytracing Contest Rendering Wada-type basins of attraction Here's a party trick for over Christmas. Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season. Fractal Dimension Calculator - FDC Box counting software for the Macintosh and Linux. Ruler or Compass Dimension Multifractal spectrum Lacunarity Recurrence plots ... Natural Fractals in Grand Canyon National Park A PowerPoint presentation by Gayla Chandler Self similarity Examples of self similarity in fractals with examples from mathematics and photos of the physical world. I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, that it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel? P. W. Atkins

19. Tessellations' Ordering Page a variety of books, puzzles, posters, videos and software related to tessellations,polyhedra, fractals, kaleidoscopes, anamorphic art, and more. http://members.cox.net/tessellations/Retail.html

Ordering Tessellations' Products A limited number of walk-in stores carry our products; if you would like to see if there is one in your area, please e-mail our U.S. Sales Office using the link below. Mail-order retailers that carry Tessellations' products include Jacobs Publishing, Educator's Outlet, Nasco, and Mindware. If you are interested in purchasing online, we recommend mathartfun.com. In addition to Tessellations' products, mathartfun carries a variety of books, puzzles, posters, videos and software related to tessellations, polyhedra, fractals, kaleidoscopes, anamorphic art, and more. Click on the logo below to go to mathartfun. U.S. sales office: Sales@tessellations.com mathartfun.com home Go to Tessellations Home Webmaster: Robert Fathauer; rob@tessellations.com

20. The Math Forum - Math Library - Polyhedra This page contains sites relating to polyhedra. tessellations, polyhedra,limits, logs, fractals (with galleries), puzzles and problems, http://mathforum.org/library/topics/polyhedra/

Browse and Search the Library Home Math Topics Geometry Higher-Dimensional Geom. : Polyhedra Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Geometric Formulas (Ask Dr. Math FAQ) - Math Forum Formulas for two-dimensional figures: triangle (equilateral, isosceles, right, scalene); quadrilateral (general, square, rectangle, parallelogram, rhombus, trapezoid, kite, cyclic and cyclic-inscriptable); regular polygon; circle (arc, segment, sector); ellipse; parabolic segment; and three-dimensional figures: rectangular parallelepiped (cube); prism; pyramid (square pyramid, frustum); regular polyhedron (tetrahedron, cube, octahedron, dodecahedron, icosahedron); cylinder (right circular); cone (right circular, frustum); sphere (sector, cap, segment, zone, lune); ellipsoid; circular torus; spherical polygon. Includes Defining Geometric Figures. more>> Naming Polygons and Polyhedra - Math Forum, Ask Dr. Math FAQ What do you call an 11-sided polygon? A 14-sided polygon? Is there a list of names of polygons? What about polyhedra? more>> Polyhedra Study - Ha Le An attempt to bring out the beauty of polyhedral study in particular and of mathematics in general via the use of the geom3d package in Maple and VRML (Virtual Reality Modelling Language). Categories: regular polyhedra; Archimedean solids; duality; facet; stellate; transformation.

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