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. |
A Fractal Christmas
Short Article from Inside Science News Service describing the basics. Includes illustrations and links. |
An Introduction to Julia and Mandelbrot Sets
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian] |
Bitshifters
Images generated by different commercial applications. Includes FAQs and tutorial. |
Chaos and Fractals: A Short Trip in Fractional Dimensions
Addresses the chaotic behavior of different attractors and their mathematical expressions. Includes plots, images and program source codes. |
Chaos Theory and Fractals
Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets. |
Chaos, Fractals, and Arcadia
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references. |
Dan Freeland
Explains the basics. Includes gallery and free software for exploring different sets and singularities. |
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 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. |
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] |
Fractals, Chaos
Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles. |
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 to Lacunarity
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications. |
Introduction: Chaos, Fractals And Attractors
Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references. |
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. |
Mandelbrot Fractals Generator
Applet to explore the Mandelbrot set in real time. |
Mandelbrot, Benoit B.
Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews. |
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. |
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. |
Sierpinski Gasket
Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references. |
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. |
The 3x+1 Fractal
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. |
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. |
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. |
The Modular Group and Fractals
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications. |
The Spanky Fractal Database
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links. |
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. |
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