Etymologie, Etimología, Étymologie, Etimologia, Etymology, (griech.) etymología, (lat.) etymologia, (esper.) etimologio
US Vereinigte Staaten von Amerika, Estados Unidos de América, États-Unis d'Amérique, Stati Uniti d'America, United States of America, (esper.) Unuigintaj Statoj de Ameriko
Fraktale Geometrie, Geometría fractal, Géométrie fractale, Geometria Frattale, Fractal Geometry, (esper.) fraktaloj geometrio

andrew-hoyer
Fraktal-Animationen mit CSS

A fractal is a essentially a geometric (mathematical) pattern. In fact, fractals can be found all around you in your every day life in things like plants, clouds, and even the blood vessels in your body!

Simply move your mouse over the fractals.

• Cantor Set: The cantor set was one of the first fractals to be studied in detail and is perhaps one of the simplest to generate. Just take a line, remove some percentage of its length from the middle (eg 1/3). Then continually repeat this process for each sub-line (each line on either side of the newly formed gap).
• Pythagoras Tree: The Pythagoras tree starts with a simple square. Next two slightly smaller squares are placed on top such that their corners match up pairwise (forming a triangle composed of two right triangles). This is then repeated for each "branch" of the tree. By moving your mouse up and down in the middle of the canvas below, a true Pythagoras tree can be seen. If the mouse is moved at all to either side, an asymmetric tree is generated.
• Koch Curve: The koch curve (if you want to call it a curve) is created by taking a line segment, dividing it into thirds and constructing an equilateral triangle in place of the center third of the original segment. An interesting fact about the Koch curve is that it has infinite length as at each step in the generation process the overall length of the line is increased by one third. As well for the math nerds out there: The Koch curve is continuous but not differentiable.
• H-Tree: An H-Tree is constructed very much like a real tree (though not random by any means). It gets it's name from the fact that when the angle between the two branches is 180 degrees, an H shape is formed. Oddly enough, this pattern has been found to be useful in designing small antenna.
• Sierpinski Carpet: The Sierpinski Carpet is created by dividing the original shape into 9 squares then removing the center square. This process is then repeated recursively for the other 8 squares. Fun fact about the Sierpinski carpet: If an infinite number of iterations is performed, the total surface area of the carpet is eventually reduced to zero.

If you're interested, click here to read about some of the implementation details.

brainpickings
The Music of Philip Glass, Visualized in Fractals

Maria Popova on the music of Philip Glass, visualized in fractals.
by Maria Popova
What fractals have to do with classical music and the secret of Einstein’s genius.
...

complexitygraphics
Fraktalartige Graphiken
Tatiana Plakhova

• SELECTED WORKS - abstract, art, illustration
• CLIENT WORKS - playboy, wired, infographic
• LIGHT BEYOND SOUND - light, structure, symmetry
• LIGHT BEYOND SOUND / video - meditation, audiovision, trip
• NOOSPHERE / video - noosphere, flight, trip
• NOOSPHERE / day images - photo, noosphere, architecture
• NOOSPHERE / night images - night, city, photo
• GEOSPHERE - geosphere, landscape, nature
• INFORMATION DIVING / video - information, data, network
• INFORMATION DIVING / images - information, infographic, graphic
• PERIODI TRIUM PLANETARUM - scheme, knowledge, diagram
• ANOTHER CALIFORNIA / video - desert, beach, nature
• ANOTHER CALIFORNIA - desert, beach, nature
• CHAOS AND STRUCTURE / video - northern circumpolar map, chaos, structure
• MUSIC IS MATH / video - audiovision, future, space
• VIOLIN / video - audiovision, music, sound
• CHAOS AND STRUCTURE / 1 - universe, chaos, structure
• CHAOS AND STRUCTURE / 2 - northern circumpolar map, chaos, structure
• MUSIC PORTRAITS / video - translation, audiovision, sound
• FOLK COMPLEXITY / video - ornament, folk, ethnic
• COMPLEXITY GRAPHICS / video - space, abstract, structure
• LINKS PROJECT / video - link, abstract, complexity
• ATMOSPHERIC - sky, atmosphere, weather
• OLD ABSTRACTS - round, scheme, paper
• MUSIC IS MATH / IMAGES - gold, sea, music
• FLOWERS IN CHAOS - flower, philosophy, abstract
• UNDERSEA - jellyfifh, sea, abstract
• BIO - bio, biology, nature
• BIO / Patterns - biology, nature, pattern
• COMPLEXITY GRAPHICS - complexity, abstract, digital
• GEO / Maps - geo, map, abstract
• FLORAL CONCEPTS - floral, pattern, nature
• MUSIC PORTRAITS - audiovision, music, rhythm
• COMPLEXITY PATTERNS - pattern, abstract, art
• LINKS PROJECT / part 1 - links, connection, network
• LINKS PROJECT / part 2 - visualization, data, abstract
• VIOLIN / Red - red, heart, love
• GEO / Textures - texture, geo, earth
• FOLK COMPLEXITY - ethnic, oriental, lamp
• FOLK COMPLEXITY / patterns - pattern, ornament, oriental

crystalinks
Fractal Geometry
Sacred Geometry

A "Fractal" is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractious meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
...

fractalspin
Mandelbot

Mandelbot Paper Toy (FREE)

Product Description

Print and cut out our friend Mandelbot, a stylish robot who just needs some help becoming 3D like the rest of us. Fold and glue him together so you two can begin to enjoy quality time together. He is a huge fan of electronic music, especially glitchy techno and algorithmic minimal 3.1415-step. Sometimes he might seem more interested in his playlist than you, but don’t take it personally - he is infinitely more happy in your presence than being alone by himself. He also enjoys the nostalgic comfort of basking in the electrostatic field of CRT computer monitors.

fractalus
Fraktale Kunstwerke

• Galleries: Damien M. Jones | Sharon Webb | Alice Kelley | Linda Allison | Kerry Mitchell | Jack & Margaret Valero | Sylvie Gallet | Mark Townsend | Paul DeCelle | Dan Kuzmenka
• Contests: 2000 | 1999 | 1998 | 1997 | Information
• Resources: Infinite Fractal Loop | Fractal Information | Fractal-Art FAQ | File Libraries | Mailing Lists | Other Fractal Sites

fractalus.com
Infinite Fractal Loop

This is the new home page of the Infinite Fractal Loop, a web ring dedicated to fractal art.

• Mandelbrot Graphical list of all sites in the Loop
• Text-only list of all sites in the Loop
• Frequently Asked Questions (FAQ)
• Join the Loop
• Loop HTML Code
• Infinite Fractal Loop News
• Loop traffic statistics
• Loop member login
• Loop admin login Phoenix
• Nova How do I use the Loop?
• What are fractals?
• How can I create fractals?
• More information about fractals
• About the Infinite Fractal Loop

The Infinite Fractal Loop Home Page | The Fractal Art Parade | Phractal Phantasies | Dave's Graphics Page | Fractal Domains Gallery | Fractal eXtreme: Mandel Louvre | Kerry Mitchell's Computer Art | Cheshire Cat Fractals | Linas' Art Gallery | Julian's Fractal Page | No-Boundary Mandelbrot Pictures | Fractal Images by Sharon Webb | Hidden Dimension | SineArt Images Offering | Sprott's Fractal Gallery | Mark's Fractal Worlds Gallery | Fractalus Galleries | FrActivity | Fractal Pages of Paul N. Lee | Sylvie Gallet's Fractal Gallery | Iterations et Flarium24 | Fractal Album | Kevin's Fractals | Karen's Fractal Gallery at Coolmath.com | Ultra Fractal Gallery | Eyebalm | Lifesmith Classic Fractals | Gumbycat's Cyberhome | IFS Gallery | an insect's colouring book | Chaoslab | Strictly Mandelbrot | Digital Diversions - Gedeon's Fractal Gallery | chaotic n-space network | Fractal-Vibes | Jacco's Fractal Pages | Fractal Art by G.W.F. Albrecht | The Mystic Dragon's Fractals | OMG Picture Gallery | T h i r d . A p e x . t o . F r a c t o v i a | Big Al's Fractals | Faye's Fractal Creations | fractius Gallery | the order of chaos | Fractals, Fractals, Fractals-brew777 | z squared plus c | Fractal Art by Philip | Flying Frog Fractals | Uncle Dan's Fractal Geometry Page | Piglette's Fractal Universe Fractal Movies | elizabyte digital art | Rooms with a View | Kevin's Fractal World | Ulli's Fractal Gallery | Tamrof's Fractal Home Page | Immrama | Paul DeCelle's Ultra Fractal Pages | Science U Fractal Gallery | Our Fractal World | Endless Spaces ... A Fractal Gallery | Fractal Dimentia | Fractals By Nous | roobarb.nu | Fractal Adventures | An Online Gallery of Synthetic Fractal Images | Arnes Fractals | Fractal Alchemy | Art and Fractals | From Chaos: Beauty - Fractal Art by Kitara | Red's Place | Emil's Fractal Gallery | Dreampaint - ebe fractales - | Chaos: A Fractal Gallery | Flat Arc Discoveries | Fractal Gallery by Ken Keller | Quintessential Sophistry Image Gallery | Trixi's Fractal Gallery | Fractal Art Galleries | The QMI Gallery | Chromatose's Fractal Garden | Fractals by dwarvenkind | Fractal Bazaar | Maria's Fractal Explorer Gallery | Soler's Fractal Site | Elements Of Design | Dreams Nightmares - Ralph's Ultra Fractal Pages | Chaos Tamed | Machida's Fractal Galleries | John Young's Fractal Pictures | Sleepy Frog Fractals | Beauty and The Beast | Linda's Fractals | Fractals by Jos Leys | InfiniteZoom Fractal Gallery | Nightingail's Gallery | The Fractal Island | Fractal Flower Garden | Makin' Magic Fractals | Anne's Fractal Menagerie | Fractal Explorer homepage | Fractals As Art | FrAcTaL LiFe | Mandel Kingdom | Pelle Evensen's fractals | Seghea | MoreZenArt | Peapod Design | Dan's Fractal Art Gallery | Arual's lil house on the peninsula - Fractalia | Fractals by Dawn | FractalZone | The Fractal Abyss | Red's Fractal Pages | Scott Hotton's Fractal Gallery | Fractal Oasis | Cliff Pickover's Fractal and Creativity Page | The Paramathematical Gallery | FEUsers Mailing List | Mackypuss | T.C. Design - Eye on Design | Tantra Pages Fractal Images Archive | Stimilon | AnaSuza Fractals | The Fractal Bargain Bin | Fractal-Dome | Rico Wack fractal gallery | Dayle D Ann.. fractal views of the Sideslippeds.. | Bee Studios | abstract-arts | Math Song | Muffin meaT GrafiX | Fractal Daydreams | Fractal Gallery Friedrich A. Lohmueller | Tiedyeman's Fractal Gallery | Fraktale von AlveoLara | DIC's Fractals World | bill's fractal factory | Fractaland | The Fantastic World Of Fractals | Collected Moments | Fractal Forum | Sciart science and art sally hunter | Lyapunov fractals | HOP - Fractals in Motion | Tennille's Fractal Page | BlueStarr | Mint's Fractal Garden | fractalogica | Fractal Art by Geoff French | ColourKitchen | Mark Hammond's World | Andrew Que's Fractals | FRACTAL FRED DE PAIVA | Imagitheque | 3D Fractals Gallery | Fractal Recursions | Fractals Campese | Amazing Seattle Fractals | Siriusworks/Richard Copeland | Just The Fracts, Ma'am

josleys.com
Leys, Jos
Mathematical Imagery by Jos Leys

Galleries :

• Vases - A collection of virtual vases, created by inverse stereographic projection of different patterns on the spherical surface of the vase. - Added on 2013-12-05
• The rabbit island - A flight over a Julia set. - Made in Ultrafractal. - Added on 2013-10-03
• L'île des lapins de Douady - A flight over a Julia set. - Made in Ultrafractal. - Added on 2013-09-25
• Mandelbrot flight #2 - A spiraling flight towards a tiny area of the Mandelbrot set. - Made in Ultrafractal. - Added on 2013-09-04
• Mandelbrot flight #1 - A flight over a tiny area of the Mandelbrot set. - Made in Ultrafractal. - Added on 2013-09-01
• Newton z^4-1 - A flight over a 3D Newton fractal (equation z^4-1=0). - Done entirely in Ultrafractal. - Added on 2013-08-20
• 3D Newton test - Experimental film, done entirely in Ultrafractal. - Added on 2013-08-18
• Catmull-Rom flight - Using Catmull-Rom splines in Fragmentarium. - Added on 2013-07-23
• Dancing circles - Iterated inversions in tangent circles create hyperbolic tilings. - Added on 2013-06-19
• Zooms - ...into the Mandelbrot set. - Added on 2013-06-19
• Mandelbrot Mountains - A zoom into a 3D Mandelbrot set. - Added on 2013-06-19
• The Julia Mountains - A flight over a 3D Julia set. - Added on 2013-06-19
• Mount Mandelbrot - A flight over a 3D Mandelbrot set. - Added on 2013-06-19
• Bach Canon on a Moebius strip - Added on 2013-06-19 -
• Hybrid 3D fractals - These were made in Ultrafractal with a combination of the Mandelbox and Mandelbulb formulas. - Added on 2013-03-14
• True 3D Kleinian groups - These limit sets of Kleinian groups were generated by three Moebius transformations with quaternion coefficients. - Added on 2013-01-05
• Hyperbolic tesselations in 3D - Two kinds of views of hyperbolic space. - Added on 2012-06-03
• 4D Polychora - Pictures made with a kaleidoscopic method for drawing 4D polychora. - Added on 2012-06-03
• 3D Newton fractals - Added on 2011-01-15
• Mandelbrot tribute 2 - ..through another 57 images in color. - Added on 2010-11-09
• Tribute to Benoît Mandelbrot - ..through 51 images. - Added on 2010-10-24
• Kaleidoscopic IFS - 32 amazing fractal 3D objects. - Added on 2010-09-07
• Mandelbox - A special kind of 3D fractal. - Added on 2010-05-28
• Hyperbolic rings and strips - Transformations of tilings in the Poincaré disc. - Added on 2010-04-22
• The Mandelbulb fractal - 36 images of this fascinating object. - Added on 2009-12-05
• 3D Fractals - A small collection of 3D Mandelbrot and Julia fractals made with various formulas. - Added on 2009-12-05
• Refraction - Un film sur la réfraction dans l'eau. - A film about refraction in water. - Added on 2009-09-17
• Hyperbolic Escher - Escher tilings converted to the hyperbolic variety. - Added on 2008-08-13
• Sculptures - Ultrafractal and Povray working together. - Added on 2008-03-04
• The shape of Planet Earth - Could the Earth have been flat after all? How about cigar shaped? Or do you prefer pear shaped? It seems it is all possible. Just a question of enough spin.. - Added on 2006-10-24
• Knots and dynamics - A collaboration with Prof. Etienne Ghys of the Ecole Normale Supérieure de Lyon, containing material presented at the International Congress of Mathematicians (Madrid, August 2006) - Added on 2006-08-23
• Knots and dynamics animations. - A collection of animations where one can see what a matrix looks like in four dimensions, how to make spaghetti using a 'horocycle', and more.. . - Added on 2006-08-23
• The Droste effect - A collection of images and animations, made with a "Droste effect" image transformation. - Added on 2006-04-17
• Escher tilings - A collection of tilings, based on the work of M.C.Escher. - Added on 2006-04-16
• Circle Packings - Kissing circles galore... - Added on 2005-09-01
• Circle packing animations - A small collection of animated circle packings - Added on 2005-08-17
• Sphere inversions Page 2 - More arrangements of spheres obtained by 3D inversion. - Added on 2005-07-01
• Hyperbolic animations - Animated hyperbolic tilings. - Added on 2005-04-18
• Animations of Kleinian group limit sets - 19 animations.. - Added on 2005-04-18
• Animations of 3D curves and surfaces - Moving curves and surfaces! - Added on 2005-04-18
• Sphere inversion animations - Some animated sphere inversions. - Added on 2005-04-17
• Doyle spirals - Hexagonal circle packings in the plane and in 3D - Added on 2005-03-02
• Strip Geometry - These images use an algorithm that draws touching circles in a strip that stretches to infinity. In some images this infinite strip was inverted into one circle.The algorithm is based on a paper by Professor Hans Herrmann of Stuttgart University, Germany. - Added on 2005-01-02
• Kleinian groups Page 5 - A collection of diverse styles.. - Added on 2004-11-12
• Sphere inversions - Sphere inversion transformations are the 3D equivalent of circle inversions. - Added on 2004-11-01
• Bubbles - These patterns are obtained by a fractal tree type algorithm. Spheres 'grow' on a base sphere, and sprout further spheres of their own. The different tree branches start to overlap and generate patterns. - Added on 2004-11-01
• Frivolous mathematical surfaces - I don't think you will find many of these in a math textbook... - Added on 2004-09-01
• Sphere packings in 3D - How does one fill a sphere with smaller spheres of various sizes so that every possible void is filled? - Added on 2004-08-20
• Raytraced Kleinian groups Page 2 - More raytracings.. - Added on 2004-06-02
• Floating Kleinian groups - Kleinian groups in an aquatic environment.. - Added on 2004-05-17
• Raytraced Kleinian groups - Added a raytracing algorithm.. - Added on 2004-05-02
• 3D Kleinian groups Page 3 - More 3D variations.. - Added on 2004-05-01
• 3D Kleinian groups Page 2 - More 3D views.. - Added on 2003-12-12
• 3D Kleinian groups Page 1 - The first 3D views of the limit sets of Kleinian groups. - Added on 2003-11-02
• Kleinian groups Page 4 - Kleinian jewelry.. - Added on 2003-11-02
• Kleinian groups Page 3 - The same algorithm, but with some more bells and whistles.. - Added on 2003-08-02
• Kleinian groups Page 2 - More early work.. - Added on 2003-07-02
• Kleinian groups Page 1 - These images where made with the first version of my algorithm. - Added on 2003-07-01
• Fun with Circles - Ford circles and circle inversions. For more information on Ford circles, visit Wikiverse Ford circle page . For more information on circle inversions, visit Wikiverse inversion page . - Added on 2003-06-01
• Impossible Geometry - With apologies to Oscar Reutersvard and M.C. Escher - Added on 2003-04-01
• Painted Spheres - Penrose tilings, Voronoi diagrams and other things, stretched over a sphere. - Added on 2003-01-01
• Hyperbolic Tilings - The Poincaré disc: the whole world compressed in a circle. - Added on 2002-11-10
• Celtic knots - A collection of Celtic knot patterns. - Added on 2002-10-19
• Fractal Tunnels - Deep in the crevices of Fractal valleys, there are tunnels. Where do they lead? What lies beyond? - Added on 2002-10-01
• Voronoi diagrams - Acknowledgments to Craig S. Kaplan , who introduced me to ornamental Voronoi designs through his paper on the subject. - Added on 2002-09-22
• Penrose tilings - Not all images follow the 'classic' Penrose tiling rules. Some were constructed allowing rhombs with smaller angles. - Added on 2002-08-01
• Tiles - Simple tiling diagrams... - Added on 2002-06-01
• The Hilbert curve - The Hilbert curve is a space-filling curve. It will eventually fill the entire plane, without ever crossing itself. - Added on 2002-06-01
• Looms - Clifford A.Pickover in his book "Keys to Infinity" has a chapter entitled "The loom of creation",in which he describes webs spun on a circular frame. One end of the wires is tied at regular intervals, but the other end moves at a different pace.The images below are made along this principle. - Added on 2002-05-01
• Exercises in Geometry Page 2 - Added on 2002-04-01
• Julia fractals - Added on 2002-03-01
• Spirals! Page 4 - The last of the spirals... - Added on 2002-02-01
• Invaders from Mars 3 - ..and they're back again!! - Added on 2002-01-04
• Invaders from Mars 2 - They're back !! - Added on 2002-01-03
• Spirals! Page 3 - Even more spirals! - Added on 2002-01-01
• Exercises in Geometry - Repetitive arrangements of polygons. - Added on 2001-11-02
• Strange Plants - These images are believed to be from an Earth-like planet, lightyears away. T - Added on 2001-11-01
• Volvox fractals Page 2 - More Volvocaceae.... - Added on 2001-10-11
• Volvox fractals - Volvox - actually a microscopic unicellular life form that lives in colonies. - Added on 2001-10-10
• Baroque Patterns - Complicated patterns from a fairly simple fractal formula.. - Added on 2001-10-06
• Spirals! Page 2 - More spirals! - Added on 2001-10-05
• Spirals! - In all shapes, but just one size.. - Added on 2001-10-04
• Alien objects - Objects that do not seem to belong here, and can only be seen through the mathematics of fractals. - Added on 2001-10-04
• String fractals Page2 - More strings! - Added on 2001-10-03
• String fractals - Stringy objects generated by fractal formulas... - Added on 2001-10-03
• Kites, birds, and other things - Stringy flying objects.. - Added on 2001-10-01
• Strange shapes - Shapes with strings and tubes.. - Added on 2001-09-03
• Magic Shapes Page 2 - More colorful fractal shapes.. - Added on 2001-09-02
• Magic Shapes - Take your pick... - Added on 2001-09-01
• Wacky Wallpapers - Hexagonal symmetry of fractal shapes.. - Added on 2001-08-01
• Magic Carpets - Magical shapes and colorful weavings... - Added on 2001-07-01
• The Dragoncurve - The Dragoncurve is the shape taken by a strip of paper that is folded many times. - Added on 2001-06-10
• Invaders from Mars - Added on 2001-06-01
• Monsters and Strange Creatures Page 5 - Strings,curls and spirals.. - Added on 2001-04-01
• Monsters and Strange Creatures Page 4 - Trap type algorithms that generate balls and strings... - Added on 2001-03-01
• Monsters and Strange Creatures Page 3 - Further explorations of different trap type colorings.. - Added on 2001-02-01
• Symmetrical creatures - All these critters have some sort of symmetry... - Added on 2001-01-01
• Monsters and Strange Creatures Page 2 - More early work in Ultrafractal, using my own trap-type coloring algorithms. - Added on 2000-11-10
• Monsters and Strange Creatures Page 1 - The second collection - Added on 2000-11-01
• Mainstream fractals - The first collection, my first explorations in Ultrafractal - Added on 2000-10-01

Articles

• 3D Kleinian groups - Posted on 2013-02-14 10:02 - An article on Kleinian groups in three dimensions, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• Comment dessiner un hécatonicosachore ? - Posted on 2012-06-03 13:26 - An article on a kaliedoscopic method for drawing 4D polychora, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France. . Read full article
• Benoît Mandelbrot, un hommage en images. - Posted on 2010-10-29 08:12 - A tribute to Benoît Mandelbrot through images published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France. Read full article
• A fractal soccer ball - Posted on 2010-06-21 12:49 - Article on kaleidoscopic 3D IFS fractals, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• Mandelbox - Posted on 2010-05-28 21:19 - Article on the Mandelbox 3D fractal, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• Ringworld - Posted on 2010-04-18 12:30 - An article about transformations of tilings in the Poincaré disc.. Read full article
• Mandelbulb - Posted on 2010-01-09 19:58 - Article on the Mandelbulb 3D fractal, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• L'effet Droste - Posted on 2009-08-24 12:51 - French language version of my article on the Droste effect, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• L'art de Francesco Mai - Posted on 2009-05-27 12:55 - Article about the work of the Italian artist Francesco Mai, published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• The hyperbolic chamber - Posted on 2008-12-29 13:38 - An article on hyperbolic geometry, first published on "Images des Mathématiques", a website of the Centre National de Recherche Scientifique (CNRS), France.. Read full article
• The mathematics behind the Droste effect. - This article uses jsMath which requires Java. - Posted on 2008-12-26 21:20 - .. Read full article
• Jos Leys, Meister der fraktalen Kunst - Posted on 2007-01-31 16:40 - Article in "Spektrum der Wissenschaft". February 2007.. Read full article
• Knots and Dynamics - Posted on 2006-08-23 13:01 - Some of the math behind the 'Knots and Dynamics' image and animation galleries. . Read full article
• ICM 2006 Benoit mandelbrot Fractal art contest - Posted on 2006-08-15 10:19 - Fractal art contest at the occasion of the International Congress of Mathematicians in Madrid, August 2006. - One of my works" was amongst 16 works chosen from over 200 entries, and these were shown at an exhibition in the Centro Cultural Conde Duque during the Congress. There was an article in El Pais (Spanish national newspaper) on this exhibition.. Read full article
• Les beautés mathématiques de Leys - Posted on 2006-04-22 18:20 - Article by Prof. Jean-Paul Delahaye in "Les nouvelles d'Archiméde",2nd quarter 2006. Read full article
• Jos Leys, un artiste géomètre. - Posted on 2006-04-22 18:17 - Article by Prof. Jean-Paul Delahaye in "Pour la Science", April 2006. Read full article
• Hexagonal circle packings and Doyle spirals - Posted on 2006-04-22 17:43 - A brief summary of the math behind Doyle spirals.. Read full article
• Sphere inversion fractals - Posted on 2005-06-22 18:46 - Article published in "Computers and Graphics"Graphics,Volume 29, Issue 3, June 2005.. Read full article

metaphorical
Blossfeldt Fractal

Blossfeldt Fractals is a dynamic composition of plant forms, based on photographs by Karl Blossfeldt, generated through algorithms similar to Lindenmayer System.

Photographs by Karl Blossfeldt are both resource and inspiration in my project. I first scanned the photos and then manually edit and dissect the different plant elements.

Then I create a custom software to import these images and tag the points of interest in them. I mark points where stems or leaves or flowers may grow, specify the magnitude and direction of each point, and classify each image by its shape and texture.

• Carousel 3D
• Cross Fade Sprite
• Taking a line for a walk
• Mosumi
• Kubist
• Layer Compose
• Layer Export
• Tween Sprite
• Alarm Bed

nikolasschiller
Fractals

skytopia
Mandelbrot Fractals 3D

The basic idea is that instead of rotating around a circle, as in the normal 2D Mandelbrot, we rotate around phi and theta in 3 dimensional spherical coordinates.

sourceforge
Fractal Zoomer

Introduction

XaoS is a fast portable real-time interactive fractal zoomer. It displays the Mandelbrot set (among other escape time fractals) and allows you zoom smoothly into the fractal. Various coloring modes are provided for both the points inside and outside the selected set. In addition, switching between Julia and Mandelbrot fractal types and on-the-fly plane switching is provided. The first version was a minimal X Window Mandelbrot viewer by Thomas later modified by Jan to support high frame-rate zooming. Other additions were later made by both Thomas and Jan including autopilot (for those of you without drivers licenses), palette changing, GIF saving, and fractal inversion.

You may be interested in viewing our small image and animation galleries and tutorial.

You can find further information in the documentation section including supported platforms, system requirements, and known bugs/limitations.

Images from tutorials
Images done using new 3d filter

An introduction to fractals

• An introduction and the Mandelbrot set
• Julia set
• "Newton's julia"
• Barnsley's julia morphing
• Barnsley's julia morphing II

stonybrook
Fractal imaging of Tic-Tac-Toe

Winning strategies, as a matter of fact, could be thought of as spatial movements through the fractal toward those winning games.

Uni Wisconsin - Madison
Pickover, Clifford A.
Fractal and Creativity Page

Here are some high-resolution images I recently computed and rendered. Most are drawn from the universe of mathematics.

| Memnoch the Devil | Quantum Foam Embedding Diagram | Worm Hole Embedding Diagram | Black Hole Embedding Diagram Showing Space Warpage | Gravitational Ripples Produced by Two Black Holes | Fractal Menger Sponge Floating in Space | Fractal Martian Landscape | Seashell Based on Logarithmic Spiral | The Infinite Curl | The Fractal Wave | E.T. Fractal | X-Files in a Bubble | Aliens are Here | Complex Rational Number Froth | Fractal Ford Froth | Space Tunnel | I Have Dreams at Night | From the X-Files | Star Trek Voyager Simulated Fossil Seashell | Synthetic Fractal Coral | Circuit Swirl | Beneath My Kitchen Sink is a Portal to a Parallel Universe | (Requires glasses from www.chromatek.com for incredible 3-D viewing.) | Telopodite Fractal 1 | Telopodite Fractal 2 | Telopodite Fractal 4 | Telopodite Fractal 3 | A Vision of the Afterlife | Forgive me Father, for I have sinned. | - Hyperspace 1 - Hyperspace 2 - Hyperspace 3 - Hyperspace 4 - Hyperspace 5 - Hyperspace 6 - Hyperspace 7 | | Message from Uranus- | Message from Neptune | Golgotha Alien Orb | God 1 | God 2 | God 3 | God 4 | God 5 | God 6 | God 7 | 3-D Space Kaleidoscope | Explore Virtual Reality Zoology with VRML | JAVA Geometry Explorer | Click image to Explore Mygalomorph Geometry in the Java Interactive Loom of Creation. Create and discover your own unique patterns. | Click image to see computer-generated cartoon faces used to display data and for assessing children. | More information on fractals and fractal experts.

wolframalpha
Fractals

Algebraic Codes

• analyze an algebraic code cyclic code 36, 2
• find codes with a given level of error correction codes that can correct 7 errors

Fractals

• draw a fractal set Koch snowflake
• draw a fractal set Sierpinski gasket
• draw a fractal set Haferman carpet

Mathematica Programming

• get usage information about a Mathematica function StringTrim
• find options for a function Dynamic options
• find groups of functions mathematica plotting functions

Image Processing

• apply a morphological operator to an image apply bottom-hat transform to trumpet image
• detect features of an image find features of shark image with radius 0.5
• perform color processing posterize galena image using 4 levels