Fractals, Chaos, SelfSimilarity
Random space filling tiling of the plane
Space filling tiling of a plane (and a line or 3D) with an arbitrary shape.
Representing geometry in SecondLife
Some comments on the suitability of SecondLife
as a way of presenting fractal geometry
Fractal forms found by using Google Earth
Readers are encouraged to contribute their own findings.
POVRay Fractal Raytracing Contest
Random walk on the plane.
Rendering Wadatype 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.
Box counting fractal dimension of volumetric data
Time exists so that not everything happens at once. Albert Einstein
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
Visualising volumetric fractals
Introduction to fractals
Perlin noise and turbulence
Creating arbitrary dimensional textures and other natural effects
using techniques credited to Ken Perlin.
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 synthesis and midpoint displacement and a
gallery of images created using Voxel World by Dmytry Lavrov.
IFS generator
Macintosh based IFS generator application and manual. Random IFS Gallery.
Colouring Attractors
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
Diffusion Limited Aggregation

DLA in 3D

Platonic solids

Tropical leaf

Random Attractors

Peano Basin

Fractal thorn

Wallpaper

Sponge and gasket

Chaos Game

Fractal linked tori

Fractal space filling

Wada

Apollony fractal

Mauldin Gasket

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

Bouali attractor

Henon Attractor

Henon Map

Henon Phase Diagrams

Star Julia

Tree roots

Attractor island

Peter de Jong

Clifford

Chen Lee Attractor

Gingerbread man

Popcorn

Clouds are not spheres, coastlines are not circles,
bark is not smooth, nor does lightning travel in straight lines.
Mandelbrot

Burning ship

Tippetts Mandelbrot

Lemon

Inside out Dragon

Marek Dragon

Buddhabrot

Mandelbrot

Julia Set

Sin Julia

Cactus

Newton Raphson

Biomorphs

Mandelbrot powers

Binocular

Guitar

"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 fiveweek Dangrabad Beta sand blizzard?"
"A fiveweek 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

Q Series

Carotid function

Computer sketching

1D Cellular Automata

Pascal modulo

Fuzzy Logic

Square tile fractal

Stretch/fold

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

Von Koch Snowflake

Multifractal

Cross (a)

Cross (b)

Pentaplexity

Tiles

Quadratic Koch Island (a)

Rings

Twon Dragon

Dragon Curve

Hexagonal Gosper

Krishna Anklets

Mango Leaf

Snake Kolam


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

Curlicue

Trianguloid

Fractal fields

Inverse tree

Lace

Diaxial Cantor Plane

Tetration

Cross Carpet

Mandelbrot factorization

Rogers Rings

Measure Function

Trifaction

Woggle

Reverse Julia

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*ri*i2+x/25,i=2*r*i+y/10,j*j+i*i<11&&k++<111;r=j);}

IFS Spiral

IFS Mandelbrotlike

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

Gauss Map IFS

Chaos:
Bounded, deterministic dynamics that are aperiodic and display
sensitive dependence to initial conditions.

LSystems

LSystem leaf

LSystem bush

LSystem bush

LSystem bush

LSystem Sticks

LSystem bush

LSystem bush

LSystem algae

LSystem algae

LSystem weed

LSystem bush




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

Multifactal Mandelbrot

Fractal Crown

Magnet 1

Magnet 2

Random shell gaskets

Kissing circles

Solenoid

Circular Infinity

Circle Squares

Zubieta Julia

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

Boxed Set

Cross menger

Jerusalem Menger

Cubic

Menger in Second Life

Hypercomplex

Quaternion Julia

Danca Fractal



Bedouin

Real valued mset

Quinternion

sinemset

Triternion






Contents :
( Index )
( All pages )

Papers, Articles, Seminars, Workshops
Data Formats: 3D, Audio, Image
Geometry, Surfaces, Curves, Polyhedra
Fractals, Chaos, Self similarity

Domes, Planetariums, Fisheye, Spherical mirror
Stereographics, 3D projection
Miscellaneous: Projection, Modelling, Rendering
Exhibitions, Posters
Fun, Puzzles, Travel

New/Updated :

Cubic fractal 
Curlicue fractal 
EqualAngle Cubemaps (EAC) 
What does it look like being on a mountain top engulfed by fire? 
Pilbara rock art: laser scanning, photogrammetry and 3D photographic reconstruction as heritage management tools 
Spatial errors in stereoscopic displays 
Visualising volumetric fractals

Offsite :


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