A fractal is a chaotic mathematic object which can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and are generally self-similar and independent of scale. In many cases a fractal can be generated by a repeating pattern, typically a recursive or iterative process. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken" / "fraction". Chaos theory, in mathematics and physics, deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions. Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder.
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code. klein.math.okstate.edu/kleinian
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. aleph0.clarku.edu/~djoyce/newton/newton.html
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets. math.bu.edu/DYSYS/dysys.html
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links. spanky.triumf.ca
Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery. www.geocities.com/fabioc
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations. math.rice.edu/~lanius/fractals/dim.html
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds. www.efg2.com/Lab/FractalsAndChaos
Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers. aleph0.clarku.edu/~djoyce/julia/explorer.html
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads. www.3dfractals.com
Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references. www.geocities.com/CapeCanaveral/Lab/5833
Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references. www.cut-the-knot.com/blue/Mandel.html
Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles. astronomy.swin.edu.au/~pbourke/fractals
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact. www.fractalfoundation.org
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations. www.ibiblio.org/e-notes/MSet/Contents.htm
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations. www.ibiblio.org/e-notes/3Dapp/Mount.htm
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian] library.thinkquest.org/26242
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