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 Polyhedra Fractals:     more detail

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Google Directory Science Math Chaos and Fractals. Directory Help Search only Geometry Formats Curves Surfaces polyhedra fractals, Chaos Projection Stereographics Colour
http://www.i-une.com/cgi-bin/meta/search.cgi?lang=en&keywords=Chaos and Frac

2. The Geometry Junkyard: Fractals
fractals. Allegria fractal and mathematically inspired jewelry S¡ndor Kabai's mathematical graphics, primarily polyhedra and 3d fractals. Labyrinth tiling
http://www.ics.uci.edu/~eppstein/junkyard/fractal.html

Extractions: 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.

3. The Geometry Junkyard: Polyhedra And Polytopes
on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex S¡ndor Kabai's mathematical graphics, primarily polyhedra and 3d fractals
http://www.ics.uci.edu/~eppstein/junkyard/polytope.html

Extractions: 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.

4. 3D Fractals
3D Fractal Generator. This is an extension of my wireframe applet. It generates 3dimensional fractals by superimposing polyhedra upon themselves recursively.
http://www.houseof3d.com/pete/applets/wireframe/fractal/

Extractions: This is an extension of my wireframe applet. It generates 3-dimensional 'fractals' by superimposing polyhedra upon themselves recursively. You get to pick the polyhedron, the level of recursion, and the spaces between the individual polyhedrons. You can set the fractal spinning by dragging on it with your mouse and releasing. If you have 3D glasses, you can use those, too. Get a damn java enabled browser, would you? gently drag and release to start the model spinning window.onerror = null unit shape : tetrahedron pyramid sextahedron octahedron cube levels : DANGER!!! PLEASE increase levels gradually - see below.) Hint - spinning cubes look way cool with lots of separation. Use CAUTION when selecting how many levels of recursion you want. A recursive tetrahedron with 5 levels contains 1,536 lines, and 6 levels has 6,144 lines. A cube with only 4 levels also has 6,144 lines (if your browser can survive it, either of these looks wild spinning slowly (with tons of space for the cube, optional for the tetrahedron)). But BE CAREFUL!

5. Help Contents / Examples / Polyhedra-fractals (3d Fractal)
polyhedrafractals (3d fractal). Help Contents Examples polyhedra-fractals (3d fractal) polyhedra-fractals (3d fractal). This example
http://www.student.uni-augsburg.de/~micheler/Elica-5.0-HTML-help-0.3/help/polyhe

Extractions: Help Contents Examples Polyhedra-fractals (3d fractal) Pascal-Assignment (simple) Pythagoras (advanced) 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. ;

6. 3D Mountains
Shows how to create fractal mountains, 3D Mandelbrot and Julia sets, convex, stellated and polyhedra. Uses tiny Java1.1 applets and VRML worlds.
http://www.ibiblio.org/e-notes/3Dapp/Mount.htm

7. Help Contents / Examples / Polyhedra-fractals (3d Fractal)
Translate this page Sorry, this version of help is intended only for browsers supporting frames.
http://www.student.uni-augsburg.de/~micheler/Elica-5.0-HTML-help-0.3/help/polyhe

8. 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

9. Mathartfun.com - Where Math, Art & Fun Come Together!
Online store and gallery of mathematical art. Browse topics including tessellations, polyhedra, fractals, anamorphic art, kaleidoscopes, M. C. Escher and Origami. Books, puzzles, posters and more
http://www.mathartfun.com/shopsite_sc/store/html

10. Amby's Education Site -- Math Puzzles & Learning Activities
performance tasks) Geometry Collage, Logic Advertisement, Tessellations, Scale Drawings, Building polyhedra, and Line Designs; Paper entitled fractals.
http://amby.com/educate/mathgame.html

Extractions: Other Math Resources EduStock Edustock is designed to teach people of all ages about the stock market. It includes: EduStock http://tqd.advanced.org/3088/welcome/welcomenf.html The Diet Problem: An Application of Linear Programming Check-off the foods you're willing to eat and the program will find the cheapest combination of them meeting a person's daily nutritional requirements. Provides numbers of servings, cost, percentages of nutrients from different sources, etc. in both table and pie chart form. PLEASE consult your doctor before embarking on any diet especially one, for example, including 10 servings of Air-Popped Popcorn!! Argonne National Laboratory Mathematics and Computer Science Division http://www.mcs.anl.gov/home/otc/Guide/CaseStudies/diet/index.html

11. Mathartfun.com Books Page
Books related to math and art. Escher, tessellations, polyhedra, fractals and more. Browse the following types of books Tessellations. polyhedra. Perspective systems. fractals. M.C.Escher
http://www.mathartfun.com/shopsite_sc/store/html/Books.html

12. Lifesmith Classic Fractals Gallery 1988-2002
Lissajou Figures(100) 3D Spherical Harmonics (215) Knots(100) polyhedra Conic Sections (115) Stellated polyhedra(45) Starface polyhedra(45) Affine
http://www.lifesmith.com/gallery.html

Extractions: Magnification! 24 images added to the 2000 X line! 22 images added to 1996 J line! 12 images added to 1988-90 A line! Selected Fractal Imagery by Series/Years (1988-2002): 2003(Y) Line 156 Images 2002(P) Line 237 Images 2001 (G) Line 270 Images 2000 (X) Line 175 Images ... Two-dimensional imagery 1988-1996 (B) 320 Images

13. Opengl
Formats. Curves. Surfaces. polyhedra. fractals, Chaos. Projection. Stereographics. Curves. Surfaces. polyhedra. fractals, Chaos. Projection. Stereographics.
http://www.babieca.com/cgi-bin/engine/smartsearch.cgi?keywords=opengl

14. The Math Forum - Math Library - Fractals
Cool Math Karen A searchable amusement park of mathematics for exploring math functions, tessellations, polyhedra, limits, logs, fractals (with galleries
http://mathforum.org/library/topics/fractals/?keyid=9511105&start_at=51&num_to_s

15. The Math Forum - Math Library - Fractals
Programs Xah Lee A listing about 40 excellent recreational math programs for Macintosh that do polyhedra and Rubic cubes, curves and surfaces, fractals and L
http://mathforum.org/library/topics/fractals/?keyid=9511105&start_at=201&num_to_

16. Art Gallery
Category Illustration Art Mathartfun.com Books, puzzles, posters and art gallery related to tessellations, polyhedra, fractals, anamorphic art, and MC Escher.
http://www.sightquest.com/search/art gallery/

17. Bookmarks fractals
polyhedra Koch s Flakes 3Dtree. http//www.people.nnov.ru/fractal/VRML/3dLsys/3Dtree.htm

Extractions: Votre portail e-Learning SOMMAIRE Pages Web Anneaux Web Demos ... Liens fractales de Markus-Lyapounov Charles Vassalo (The infinite fractal loop) Fractalismes Fantastic Fractals Stochastic Resonance Perugia (Italy) Chaos Club Definition of Polymer, P-System, Metapolymer and Pseudopolymer, etc 3D VRML Lab 3D fractals autre adresse Cantor's Polyhedra Koch's Flakes Flight From Fractal Ultra Fractal Ultra Fractal is a Windows program that creates images of fractals. Fractals by Jos Leys The Monsters and Strange Creatures Galleries The Geometry Galleries Animations Iterations et Flarium24 Into the Mystic Fractal ViZion 1.20, Fractal Zplot 1.21 and Dofo-Zon Elite 1.21 Fractal eXtreme Fractal Pages African Fractals by Ron Eglash Infinite Folds Peter Budai - Origami - fascinating self-similar folds Index to Named Fractals Stewart R. Hinsley

18. Final Project
Some topic ideas the ninepoint circle, linear perspective, polyhedra, fractals, conic sections, elliptic geometry, projective geometry, inversion, finite
http://cas.bellarmine.edu/fenton/Geometry/Final_Project.htm

Extractions: MATH 305 Modern Geometry FINAL PROJECT This is in two parts: A paper, due Thursday May 1 points A presentation to the class, Thursday May 1 points Find a geometric topic not covered in class. This can be something related to what we have studied or something completely new. It could be something you might teach in the future. The College Mathematics Journal or Mathematics Teacher are good sources for ideas. (I believe both are available in our library, and other journals as well.) The goal is for you to teach yourself something new about geometry and then present it to others. Please discuss your topic with me before you prepare your materials. Here are some specific requirements: The paper should be at least four and no more than six pages, double-spaced in 12-pt. font. If you use lots of diagrams, your paper should be closer to six pages than to four pages. The paper and the presentation should include at least one major theorem on that topic. (The proof is optional.) Turn in two copies of your paper.

19. Japanese FAQ
3D IFS fractals are 3D analogous to 2D IFS fractals using polyhedra instead of polygons. ie Menger sponge is 3D analogous to Sierpinski Carpet.
http://www.fractal3d.com/faq/faq.html

Extractions: What is a fractal? Fractal is a word invented by Benoit Mandelbrot to specify the complicated phenomena of shapes with self-similarity. According Benoit Mandelbrot words in his book, The Fractal Geometry of Nature, "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragents. It is therefore sensible - and how appropriate for our needs! - that, in addition to "fragmented" (as in fraction or refraction), fractus should also mean "irregular," both meanings being preserved in fragment." Other descriptions on fractals can be found from the following links: http://www.faqs.org/faqs/sci/fractals-faq/ sci.fractals FAQ (Q2: What is a fractal?) http://mathworld.wolfram.com/Fractal.html fractal: ERIC WEISSTEIN'S world of MATHEMATICS What is fractal3D? Fractal3D (www.fractal3D.com) is the world's first web site which provides information and products of great new finding 3D quasi-fuchsian fractals in pure mathematics. What is quasi-fuchsian fractals?