Fractals, Chaos
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
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.
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 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

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

Von 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

Square tile fractal

Pascal modulo

Diaxial Cantor Plane

Tetration

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*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

Mauldin Gasket

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

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

sinemset

Boxed Set

Cross menger

Danca Fractal

Tippetts Mandelbrot

Menger in Second Life

Fractal linked tori

Fractal space filling

Gauss Map IFS

Jerusalem Menger Cube







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
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
Contents :


Index
Papers, Articles, Seminars, Workshops
Data Formats: 3D, audio, image
Geometry, Surfaces, Curves, Polyhedra
Fractals, Chaos, self similarity
Texture, Colour, Tiling

Exhibitions, competitions, productions
Domes, planetariums, fisheye, spherical mirror
Stereographics, 3D projection
Miscellaneous: Projection, Modelling, Rendering
Fun, Puzzles, Travel
Old stuff, historical interest only

New :


Fun with a drone
Slit Scan photography
Chronopanorama (Time lapse panoramas)
MobiusStripLike Columnar Functional Connections are Revealed in ...

Presenting :


Workshop: 3D Image Visualisation and Model Generation with Simpleware
Novel physical representations for the visualisation of science data and mathematics. April 2015

Search :




The contents of this web site are © Copyright Paul Bourke or
a third party contributor where indicated.
You may print or save an electronic copy of parts of this web site
for your own personal use.
Permission must be sought for any other use.
Any source code found here may be freely used provided credits are given
to the author.

