Fractals are an amazing mathematical tool that has in recent decades led to advances in medicine, geology, music and other art forms. A rough description of a fractal is that of a geometric shape that, when split in to parts approximately represent a reduced copy of the whole. Confused? Perhaps Benoit Mandelbrot, the french mathematician who coined the term might be familiar to you.
Collected here are a selection of links to information on Fractals split in to several sub-catagories.
Enjoy!
(These links and descriptions fulfill the requirements for the “Annonated Links” assignment for 2806ART, Griffith University Gold Coast, 2008 – Andrew Nesvadba 1586583)
FRACTALS 101
math.rice.edu
A Math Teacher’s classroom guide to Fractals
http://math.rice.edu/~lanius/fractals/WHY/
Cynthia Lanius provides a step-by-step classroom plan for math teachers to introduce the concept and application of fractals. Included are guides on creating some easy fractal sets and introduction to higher concepts such as “Fractal Dimensions”. A great aide and an easy introduction to Fractals.
http://www.cnspace.net
Chaotic n-space network
http://www.cnspace.net/html/fractals_intro.html
A simple website introducing fractal concepts and their application in art. Includes a selection of galleries with examples of different fractal designs and software to generate your own at home. A great jumping point for artists intent on using fractals in their work.
http://www.ecometry.biz
Patterns and Fractals
http://www.ecometry.biz/patterns.htm
Ecometry is dedicated to understanding how the economy operates in countries by applying concepts of patterns and attractors to the systems. Included is this page full of a large variety of fractals patterns including text based recursion and links to more advanced topics at the end. While not directly informative, it provides a diverse collection of examples with which to understand the concept of fractals.
http://www.arcytech.org
Fractals: An Introductory Lesson
http://www.arcytech.org/java/fractals/intro.shtml
Yet another lesson planner, this one including java-scripted examples (be careful, some are prone to crashing if iterations are taken too far) and a keyword based method of hiding answers to classroom questions. This gives a very broad overview of fractals while scaling to advanced concepts step-by-step.
classes.yale.edu
Fractal Geometry
http://classes.yale.edu/fractals/
A more advanced primer from Yale in to fractals. Delve in to this page at the risk of wasting hours discovering just how fractals are useful to us in advancing not only science, but also art. It’s so easy, even kids can understand it!
http://www.fractalwisdom.com
Fractal Geometry: The Story of Benoit B. Mandelbrot and the Geometry of Chaos
http://www.fractalwisdom.com/FractalWisdom/fractal.html
Lastly, a quick bio of the man who not only coined the term “Fractals” but also became synonymous with them thanks to his famous design. This is less of an informative piece on fractals directly and more on the man and the science that drove him.
FRACTALS IN SCIENCE
news.research.ohiou.edu
Scientists Create the First Synthetic…
http://news.research.ohiou.edu/news/index.php?item=298
The development of fractal molecular structures is an important step in the realisation of nano-machines, science fiction is slowly becoming science reality. Two years ago, scientists managed to develop one of the largest fractal molecules and its impact on technology could be revolutionary for energy storage.
mitworld.mit.edu
Fractals in Science, Engineering and Finance (Roughness and Beauty)
http://mitworld.mit.edu/video/52/
This special lecture by Benoit Mandelbrot is a lengthy but absorbing look in to how fractals have helped and will continue to help science. The full lecture is over one hour and recorded in Real-Player video format.
Tenthdimension.com
Imagining the Tenth Dimension
http://www.tenthdimension.com/medialinks.php
This fascinating short-film delves in to multi-dimensional theory so simply you’ll think it has to be a joke. Rob Bryanton’s book is anything but that and attempts to explain the fractal nature of our universe without caving your head in with heavy theory. This is a highly recommended viewing.
Newscientist.com
Galaxy map hints at fractal universe
Modelling of the universe, potentially a map of how things got where they are and where they may end up. Could this mean a rewrite of how we perceive our universe? Or is this just the end result of a friendly wager between scientists. A fascinating recent glimpse in to fractals in science.
FRACTALS IN SOCIETY
http://www.ralph-abraham.org
HUMAN FRACTALS: THE ARABESQUE IN OUR MIND
http://www.ralph-abraham.org/articles/MS%2373.Cyborg/fractals.html
This is a quick primer in to social science and its use of fractal modelling. Fractals are fascinating in their application across many disciplines, including that of social theory and how human beings – en masse – can be described using these models. Throughout history and even today, remnants of human beings and their attraction to living in a fractal manner is evident.
Emis.de
Review of Eglash’s “African Fractals: Modern Computing and Indigenous Design”
http://www.emis.de/journals/NNJ/reviews_v2n4-Bangura.html
In no other society is the evidence of humans perpetuating a fractal method of arranging their lives more apparent than in that of African society. Although a review on the book, it covers some of the basic points and may inspire you to check out the book from your local library.
VisualComplexity.com
Web Trend Map 3.0
http://www.visualcomplexity.com/vc/project_details.cfm?id=547&index=547&domain=
Visual Complexity is a wonderful site that contains a multitude of examples demonstrating the application of fractal modelling in a social setting. Web Trend Map manages to represent the interconnectedness and complexity of viewing habits on the internet. Once you have finished with this toy, explore the many other examples on offer here.
itre.cis.upenn.edu
Language Log: The fractal theory of Canada
http://itre.cis.upenn.edu/~myl/languagelog/archives/005497.html
This is more of an amusing post than anything else, but it attempts to prove that thanks to fractal theory, everything we know is Canadian. Although this can be applied to almost anything, I like to think that this site can be my excuse for mistaking the Canadian accent for a Washington State accent.
FRACTALS IN GAMING
sprott.physics.wisc.edu
Fractal Fantasies Game
http://sprott.physics.wisc.edu/pickover/pc/fractal-fantasies.html
A board game developed by bored scientists and mathematicians to tickle their fancy. Check it out and make it for yourself!
ProFantasy.com
Fractal Terrains: Random Planet Generation
http://www.profantasy.com/products/ft.asp
This video game could better be described as a desktop toy, allowing users to randomly generate an entire planet complete with weather systems. Here, modelling of natural environments using fractal theory is taken to a commercial level. Interesting to check out.
Gamasutra.com
Towards More Meaningful Games
http://www.gamasutra.com/view/feature/3736/towards_more_meaningful_games_a_.php
Although not directly mentioned, game development – especially for that of a role-playing or adventure game – can take on the appearance of a fractal design. As choices lead to consequences and emotions of players are played with, how does a developer manage to create a sense of freedom and independence without destroying the illusion with poorly ended sequences. A fascinating article by one of the writers for “The Witcher”.
YoYoGames.com
Fractal Fighter
http://gmc.yoyogames.com/index.php?showtopic=307000
A downloadable game created using Game Maker for a recent competition. This bullet-hell shoot’em’up game is not for the feint of heart and will test your skill, patience and computer.
GameProgrammer.com
Generating Random Fractal Terrain
http://www.gameprogrammer.com/fractal.html
For those interested in the nitty-gritty of fractal theory and game design, here’s how to do it at home for yourself. Not for those without an interest in game programming.
FRACTALS IN NATURE
ScienceNews.org
The Mathematical Lives of Plants
http://www.sciencenews.org/view/generic/id/8479/title/The_Mathematical_Lives_of_Plants
The Fibonacci sequence and others are examples of how mathematics has attempted to model the natural world. Or could it be the other way around? Does nature truly depend on these mathematical concepts to survive?
classes.yale.edu
How the Leopard Gets Its Spots; How the Zebra Gets Its Stripes
http://classes.yale.edu/Fractals/Panorama/Biology/Leopard/Leopard.html
This technical article attempts to demonstrate how a simple fractal model could be responsible for how these animals develop their distinctive coats – including how they may be uniquely created.
http://www.ba.infn.it
Nature Fractals
http://www.ba.infn.it/~zito/project/nfractals.html
Another small collection of natural phenomena representing fractal models. Although small, it does include some unique examples beyond the usual Broccoli.
Migel.com
Naturally Occurring Fractals
http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html
Yet another collection with a difference – some stunning examples of bacterial and viral colonies. Not only that, some beautiful examples of artwork showing similarities between the natural world and “randomly generated” art.
davis.wpi.edu
Exploring Fractal Islands
http://davis.wpi.edu/~matt/courses/fractals/islands.html
This article is one in a series dedicated to demonstrating the mathematical theory behind modelling natural phenomena. Fractal Islands outlines the creation of islands (and possibly continents) from random models. Complimentary to this previous link.
FRACTALS IN ART (and music)
ColourLovers.com
Fractal Art: Complex and Beautiful Color Inspiration
http://www.colourlovers.com/blog/2008/08/29/fractal-art-complex-and-beautiful-color-inspiration/
This article is a stunning and comprehensive collection of amazing artwork. Wether it’s married with unnatural colourings or a stunning merger with satellite photography, this collection of artwork pops with vibrancy and can even make you a bit squeemish. Flikr links and videos are also included here.
FractalArtContests.com
Benoit Mandelbrot Fractal Art Contest: 2007 Winners
http://www.fractalartcontests.com/2007/winners.php
If you needed some more eye popping artwork to gawk at, here it is. The variety of styles represented here is amazing and belies the complexity of mathematics used to develop it.
FractalArts.com
Fractal Art Tutorial
http://fractalarts.com/ASF/Tutor1.html
Want to try your hand at creating art like those in the galleries above? If you have the chops to mix formulas with your creative juices, take a dive in to this in depth series of articles with the how-tos and the links to programs you’ll need to give this a try.
hektor.umcs.lublin.pl
Modular Origami — Fractals, IFS
http://hektor.umcs.lublin.pl/~mikosmul/origami/fractals.html
Like to work with your hands? Fancy yourself a bit of an origami ninja? Take a crack at trying to make fractal models like these see just how large you can make it!
BrothersTechnology.com
Fractal Music
http://www.brotherstechnology.com/math/fractal-music.html
That’s right, even MUSIC is being generated using fractal models. Here you can find some examples (maybe not to your taste) and links to more information about artists and HOW-TO do it for yourself. A fascinating, if not exciting, artistic branch.Fractal Art Tutorial
physics.physorg.com
Jackson Pollock’s art and fractal analysis
http://physics.physorg.com/news84452049.html
Fractal modelling has been suggested as a method of analysing and creating a “key” or “signature” for artists, something that regardless of their work can be used to prove it was made by that artist and that artist only. Tested on Jackson Pollock’s work, it may not be as fool proof as it seems.
Cameronius.com
Figures for “Impossible Fractals”
http://www.cameronius.com/graphics/impossible-fractals-figures/
Lastly, this is more of a fun site combining popular “impossible” imagery with fractal modelling. This is mind bending artwork squared.
Fractal Fracas 
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