From the archives

The Winter of Discontent, 30 years on

news.bbc.co.uk

McCain vows to fight to change US

John McCain promises "change is coming" as he accepts the Republican party's candidacy for the White House.

news.bbc.co.uk

Keegan resigns as Newcastle boss

Kevin Keegan quits as manager of Newcastle after just eight months in charge.

news.bbc.co.uk

Black to green

Germany pilots technology to clean up coal power

news.bbc.co.uk

Adults 'rely on parents' finance'

Parents support their grown-up children to the tune of £21,500 in the years after they turn 18, a study suggests.

news.bbc.co.uk

Toon Army talks

Anger of fans at Keegan's departure

news.bbc.co.uk

Brown 'backs more Holyrood power'

The SNP claims that Gordon Brown is "caving in to pressure" to concede more powers to Holyrood.

news.bbc.co.uk

New governor general in Australia

Quentin Bryce is sworn in as Australia's governor general, the first woman to serve as Queen Elizabeth's representative there.

news.bbc.co.uk

Copter rescue amid flood warnings

A rescue helicopter reaches a motorist trapped by rising water, as severe weather warnings are given across Wales.

news.bbc.co.uk

Rice set for historic Libya visit

Condoleezza Rice will meet Libya's Gaddafi in the latest step aimed at improving relations between the former enemies.

news.bbc.co.uk

Global stock markets still jumpy

Fears about a global economic slowdown continue to weigh on stock markets, with Japan's main share index falling nearly 3%.

news.bbc.co.uk

DJs criticised for drink comments

A report criticises a number of radio presenters for encouraging heavy drinking among their listeners.

news.bbc.co.uk

From a height

How to survive a bellyflop into just a foot of water

news.bbc.co.uk

Crime crackdown sees 109 arrests

A summer crackdown on burglary and other crimes in Belfast has led to over 100 arrests, police reveal.

news.bbc.co.uk

England defeats hurt us - Barry

Midfirelder Gareth Barry rubbishes suggestions that England players care more about their club than their country.

news.bbc.co.uk

WWII 'remains' in jungle prove to be vines

The suspected remains of a WWII airman discovered in the Papua New Guinea jungle are the moss-covered branches of a tree.

news.bbc.co.uk

Government warned over fuel costs

A Labour backbencher warns the government faces public hostility if it doesn't provide help for voters to pay energy bills.

news.bbc.co.uk

Google is 10

What is the secret behind Google's huge success?

news.bbc.co.uk

Hoy angry at political 'cash-ins'

Olympic cycling hero Chris Hoy says he feels politicians have attempted to "cash in" on his success in Beijing.

news.bbc.co.uk

UK food prices show 8.3% increase

UK food prices have risen by 8.3% on average since January, with meat and fish up 23%, according to a study for the BBC.

news.bbc.co.uk

Sex killer 'could not be stopped'

A stalker who killed his ex-lover and then had sex with her corpse could not have been stopped, a report finds.

news.bbc.co.uk

In pictures

Haiti struggles after storms kill 170 people

news.bbc.co.uk

A gentle heavy metal fan? How music defines personality

Musical taste and style is closely related to personality type, according to new research from a Scottish university.

news.bbc.co.uk

Djokovic sets up Federer showdown

Novak Djokovic beats Andy Roddick in four sets and will now meet defending champion Roger Federer for a place in the US Open final.

news.bbc.co.uk

What do you want to talk about?

What do you want the world to talk about?

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 World Catalog > Science > Math > Chaos and Fractals

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World Catalog > Science > Math > Chaos and Fractals

Chaos and Fractals:

Bitshifters

Images generated by different commercial applications. Includes FAQs and tutorial.

http://bitshifters.com/fractal.html

Chaos, Fractals, and Arcadia

Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.

http://math.bu.edu/DYSYS/arcadia/

Graand

Free Classified Ads Portal

www.graand.com

3D Fractals Bicomplex Dynamics

Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.

http://www.3dfractals.com/

3D Mountains

Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.

http://www.ibiblio.org/e-notes/3Dapp/Mount.htm

Dan Freeland

Explains the basics. Includes gallery and free software for exploring different sets and singularities.

http://homepage.ntlworld.com/daniel.freeland/

The Dynamical Systems and Technology Project

Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.

http://math.bu.edu/DYSYS/dysys.html

The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models

Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.

http://www.geocities.com/CapeCanaveral/Lab/5833/

Efg's Computer Lab: Fractals and Chaos

Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.

http://www.efg2.com/Lab/FractalsAndChaos

Fractal Brownian Archipelago

Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.

http://swiss.csail.mit.edu/~rauch/islands/

Fractal Dimensions

Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.

http://math.rice.edu/~lanius/fractals/dim.html

Fractal Explorer

Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.

http://www.geocities.com/fabioc/

Fractal Foundation

Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact.

http://www.fractalfoundation.org

Fractal Map

Interactive online Mandelbrot and Julia generator.

http://frac.samurajdata.se/

Fractals and Multi Layer Coloring Algorithms

Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.

http://www.mi.sanu.ac.yu/vismath/javier1

Fractals Unleashed

Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]

http://library.thinkquest.org/26242/

Homepage of Kristian Gustavsson

Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.

http://www.dd.chalmers.se/~f99krgu/main/index.html

IFS Attractors

Index and definition of different attractors. Includes images, plots and glossary.

http://www.meden.demon.co.uk/Fractals/fractals.html

Images From Chaos

Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.

http://www.cps.unizar.es/~jlsubias/

Introduction: Chaos, Fractals And Attractors

Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.

http://www.ecometry.biz/

An Introduction to Julia and Mandelbrot Sets

Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]

http://www.geocities.com/leibowitz.geo/fract_en.html

Introduction to Lacunarity

Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.

http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html

Iterations and the Mandelbrot Set

Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references.

http://www.cut-the-knot.com/blue/Mandel.html

Julia and Mandelbrot Set Explorer

Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.

http://aleph0.clarku.edu/~djoyce/julia/explorer.html

Kleinian Groups Pictures

Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.

http://klein.math.okstate.edu/kleinian/

The Mandelbrot and Julia Sets Anatomy

Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.

http://www.ibiblio.org/e-notes/MSet/Contents.htm

Mathematical Figures Using Mathematica

Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.

http://mathforum.org/advanced/robertd/

Mathematics: Stilldreamer

Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.

http://www.stilldreamer.com/mathematics/

The Modular Group and Fractals

Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.

http://www.linas.org/math/sl2z.html

NASA: Fractal Clouds

Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.

http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html

Newton Basins

Article about the basins of attraction for the Newton's method for finding roots of equations and their resulting representation in the complex plane. Includes mathematical framework and examples.

http://aleph0.clarku.edu/~djoyce/newton/newton.html

Project Fractales

Research group at the INRIA national research center, France. Includes research details, publications and software.

http://complex.inria.fr/

Quantum Jumps, EEQT and the Five Platonic Fractals

Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.

http://quantumfuture.net/quantum_future/papers/qfract/

The Spanky Fractal Database

Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.

http://spanky.triumf.ca/

Technocosm

Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.

http://technocosm.org/chaos/

Tetrabrot Fractal Videos

Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.

http://www.javaspider.com/jfract

Wikipedia: Fractals

Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.

http://en.wikipedia.org/wiki/Fractals

The 3x+1 Fractal

Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. (June 1, 2004)

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYG-4C47CDM-5&_coverDate=06%2F30%2F2004&_alid=262438467&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5618&_sort=d&view=c&_acct=C000043379&_version=1&_urlVersion=0&_userid=791130&md5=92c370a59ff53edd249c27a91b0ed72e

A Fractal Christmas

Short Article from Inside Science News Service describing the basics. Includes illustrations and links. (December 1, 2003)

http://www.aip.org/isns/reports/2003/086.html

From the archives

The Winter of Discontent, 30 years on

news.bbc.co.uk

Keegan resigns as Newcastle boss

Kevin Keegan quits as manager of Newcastle after just eight months in charge.

news.bbc.co.uk

Sex killer 'could not be stopped'

A stalker who killed his ex-lover and then had sex with her corpse could not have been stopped, a report finds.

news.bbc.co.uk

What do you want to talk about?

What do you want the world to talk about?

news.bbc.co.uk

Copter rescue amid flood warnings

A rescue helicopter reaches a motorist trapped by rising water, as severe weather warnings are given across Wales.

news.bbc.co.uk

Global stock markets still jumpy

Fears about a global economic slowdown continue to weigh on stock markets, with Japan's main share index falling nearly 3%.

news.bbc.co.uk

Brown 'backs more Holyrood power'

The SNP claims that Gordon Brown is "caving in to pressure" to concede more powers to Holyrood.

news.bbc.co.uk

UK food prices show 8.3% increase

UK food prices have risen by 8.3% on average since January, with meat and fish up 23%, according to a study for the BBC.

news.bbc.co.uk

New governor general in Australia

Quentin Bryce is sworn in as Australia's governor general, the first woman to serve as Queen Elizabeth's representative there.

news.bbc.co.uk

Toon Army talks

Anger of fans at Keegan's departure

news.bbc.co.uk

From a height

How to survive a bellyflop into just a foot of water

news.bbc.co.uk

Government warned over fuel costs

A Labour backbencher warns the government faces public hostility if it doesn't provide help for voters to pay energy bills.

news.bbc.co.uk

McCain vows to fight to change US

John McCain promises "change is coming" as he accepts the Republican party's candidacy for the White House.

news.bbc.co.uk

Hoy angry at political 'cash-ins'

Olympic cycling hero Chris Hoy says he feels politicians have attempted to "cash in" on his success in Beijing.

news.bbc.co.uk

Rice set for historic Libya visit

Condoleezza Rice will meet Libya's Gaddafi in the latest step aimed at improving relations between the former enemies.

news.bbc.co.uk

Djokovic sets up Federer showdown

Novak Djokovic beats Andy Roddick in four sets and will now meet defending champion Roger Federer for a place in the US Open final.

news.bbc.co.uk

DJs criticised for drink comments

A report criticises a number of radio presenters for encouraging heavy drinking among their listeners.

news.bbc.co.uk

Google is 10

What is the secret behind Google's huge success?

news.bbc.co.uk

WWII 'remains' in jungle prove to be vines

The suspected remains of a WWII airman discovered in the Papua New Guinea jungle are the moss-covered branches of a tree.

news.bbc.co.uk

Adults 'rely on parents' finance'

Parents support their grown-up children to the tune of £21,500 in the years after they turn 18, a study suggests.

news.bbc.co.uk

Black to green

Germany pilots technology to clean up coal power

news.bbc.co.uk

In pictures

Haiti struggles after storms kill 170 people

news.bbc.co.uk

England defeats hurt us - Barry

Midfirelder Gareth Barry rubbishes suggestions that England players care more about their club than their country.

news.bbc.co.uk

Crime crackdown sees 109 arrests

A summer crackdown on burglary and other crimes in Belfast has led to over 100 arrests, police reveal.

news.bbc.co.uk

A gentle heavy metal fan? How music defines personality

Musical taste and style is closely related to personality type, according to new research from a Scottish university.

news.bbc.co.uk