Science: Math: Chaos_and_Fractals
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Fractal Geometry
- Comprehensive educational resource on the mathematical framework and formalism from the Yale University, covering the concept of self similarity. Includes topical examples, images, algorithms and softwares.
Mandelbrot, Benoit B.
- Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.
Bitshifters
Images generated by different commercial applications. Includes FAQs and tutorial.
Chaos, Fractals, and Arcadia
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
3D Fractals Bicomplex Dynamics
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
3D Mountains
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
Dan Freeland
Explains the basics. Includes gallery and free software for exploring different sets and singularities.
The Dynamical Systems and Technology Project
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
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.
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.
Fractal Brownian Archipelago
Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
Fractal Dimensions
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.
Fractal Explorer
Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
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.
Fractal Map
Interactive online Mandelbrot and Julia generator.
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.
Fractals and Scale
Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
Fractals Unleashed
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
Homepage of Kristian Gustavsson
Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
IFS Attractors
Index and definition of different attractors. Includes images, plots and glossary.
Images From Chaos
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
Introduction: Chaos, Fractals And Attractors
Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
An Introduction to Julia and Mandelbrot Sets
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
Introduction to Lacunarity
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
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.
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.
Kleinian Groups Pictures
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
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.
Mathematical Figures Using Mathematica
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
Mathematics: Stilldreamer
Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
The Modular Group and Fractals
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
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.
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.
Project Fractales
Research group at the INRIA national research center, France. Includes research details, publications and software.
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.
The Spanky Fractal Database
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
Technocosm
Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
Tetrabrot Fractal Videos
Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.
What are Fractals?
Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
Wikipedia: Fractals
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
The 3x+1 Fractal
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. (June 1, 2004)
A Fractal Christmas
Short Article from Inside Science News Service describing the basics. Includes illustrations and links. (December 1, 2003)
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