Fractals, Chaos

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 and Self Similarity
A particular box counting software package, Ruler or Compass Dimension, Lacunarity, Multifractal spectrum, Recurrence plots, Self Similarity. Examples of self similarity in fractals with examples from mathematics and photos of the physical world.

Time exists so that not everything happens at once.

By Gayla Chandler
   Natural Fractals in Grand Canyon National Park
   Fractals: A Symmetry Approach
   Gasket Photography

Fractals and Computer Graphics
Interface Magazine Article

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

Diffusion Limited Aggregation	DLA in 3D	Platonic solids	Tropical leaf	Random Attractors
Marketing idea: A potato chip in the shape of the Sierpinski gasket! It would infinitely crispy but have zero calories.
Duffing Attractor	Lorenz Attractor	Rossler Attractor	Wallpaper	Henon Attractor
Henon Map	Henon Phase Diagrams	Star Julia	Tree roots	Attractor island
Peter de Jong	Clifford	Quinternion	Fractal thorn	Triternion
Clouds are not spheres, coastlines are not circles, bark is not smooth, nor does lightning travel in straight lines. Mandelbrot
Burning ship	Real valued mset	Lemon	Insideout Dragon	Marek Dragon
Buddhabrot	Mandelbrot	Julia Set	Sin Julia	Cactus
Newton Raphson	Biomorphs	Mandelbrot powers	Q Series	Carotid function
"And are you not", said Fook leaning anxiously forward, "a greater analyst than the Googleplex Star Thinker in the Seventh Galaxy of Light and Ingenuity which can calculate the trajectory of every single dust particle throughout a five-week Dangrabad Beta sand blizzard?" "A five-week sand blizzard?" said Deep Thought haughtily. "You ask this of me who have contemplated the very vectors of the atoms in the Big Bang itself? Molest me not with this pocket calculator stuff." Douglas Adams
Logistic Equation	Oneness	Dragon Curve	Hexagonal Gosper	Gingerbread man
I am so in favour of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Georg Cantor
Triangle	Peano Curve	Crystal	Square Sierpinski	Quadratic Gosper
Hilbert	Board	Koch Curve	Quadratic Koch Island (b)	Quadratic Snowflake
Sierpinski Arrowhead	Van Koch Snowflake	Multifractal	Cross (a)	Cross (b)
Pentaplexity	Tiles	Quadratic Koch Island (a)	Rings	Twon Dragon
Is the human story largely a deterministic tale of civilisations marching to Toynbee's tune, three and a half beats to disintegration, or did the hinge of history turn on the length of Cleopatra's nose? Robert May
Inverse San Marco Dragon	Grinch Dragon	Ikeda	Pascal Grey Code	Cooral Dragon
Tiled Dragon	Fuzzy Logic	Trianguloid	Fractal fields
Pascal modulo	Diaxial Cantor Plane		Cross Carpet	Mandelbrot factorization
Rogers Rings	Measure Function	1D Cellular Automata	Lace	Reverse Julia
Trifaction	Woggle	Inverse tree	Guitar	Binocular
main(k){float i,j,r,x,y=-16;while(puts(""),y++<15) for(x=0;x++<84;putchar(" .:-;!/>)|&IH%*#"[k&15])) for(i=k=r=0;j=r*r-i*i-2+x/25,i=2*r*i+y/10,j*j+i*i<11&&k++<111;r=j);}
IFS Spiral	IFS Mandelbrot-like	IFS tree	IFS Tree	IFS leaf
IFS Sand Dollar	IFS Tree	IFS Tree	IFS fern	IFS fern
IFS Dragon	IFS Twig	IFS star	IFS Christmas tree	IFS Curve
IFS Maple leaf	IFS Chaos Text	3D IFS bush	IFS Tile	Mauldin Gasket
Chaos: Bounded, deterministic dynamics that are aperiodic and display sensitive dependence to initial conditions.
L-Systems	L-System leaf	L-System bush	L-System bush	L-System bush
L-System Sticks	L-System bush	L-System bush	L-System algae	L-System algae
L-System weed	L-System bush	Popcorn	Computer sketching	Stretch/fold
I believe the geometric proportion served the creator as an idea when He introduced the continuous generation of similar objects from similar objects. Johannes Kepler
Keplerian Fractals	Octahedral Sierpinski Carpet	3D IFS hedgehog	Sierpinski Carpet	3D IFS Cross
Quaternion Julia	Fractal Crown	Multifactal Mandelbrot	Kissing circles	Apollony fractal
The real world was full of larger structures, smaller structures, simpler and more complex structures than the tiny portion comprising sentient creatures and their societies, and it required a profound myopia of scale and similarity to believe that everything beyond this shallow layer could be ignored. Greg Egan, Diaspora
Circle Squares	Circular Infinity	Solenoid	Wada	sine-mset
Boxed Set	Cross menger	Danca Fractal	Tippetts Mandelbrot	Menger in Second Life

The Pale Blue Dot from Space - Earth. “That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every superstar, every supreme leader, every saint and sinner in the history of our species lived there - on a mote of dust suspended in a sunbeam.” Carl Sagan

Introduction to fractals

Gallery of fractal images

Generating noise with different power spectra laws
Including 1/f noise. Fractal planets and landscapes: Methods for creating fractal planets, landscapes, and clouds. Including frequency sythesis and midpoint displayment and a gallery of images created using Voxel World by Dmytry Lavrov.

IFS generator
Macintosh based IFS generator application and manual. Random IFS Gallery.

Sponge and Gasket
Description of two fractal objects and POVRay renderings by Angelo Pesce.

Colouring Attractors

New :   Small scale stereoscopic image capture Unity and Blender games in the iDome Little planet projections         Announcements :   OzViz 2009
Index Papers, Articles, Seminars Exhibitions Data Formats Geometry, Surfaces, Curves, Polyhedra Fractals, Chaos Texture, Colour Miscellaneous: Projection, Modelling, Rendering     Spherical mirror     Dome/fisheye     Stereographics Fun, Puzzles, Travel Old stuff
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