Chaos and Fractals Math Science

@Intermall

Top: Science: Math: Chaos_and_Fractals:

• Top/Science/Math/Differential Equations/Dynamical Systems
• Top/Science/Math/Applications/Complex Systems

• - Gallery and program with source. Includes animated three-dimensional sets and attractors.
  
• - Interactive online Mandelbrot and Julia generator.
  
• - Applet to explore the Mandelbrot set in real time.
  
• - Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.
  
• - Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles.
  
• - Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
  
• - Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
  
• - Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
  
• - Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
  
• - Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
  
• - Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
  
• - Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
  
• - Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
  
• - Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
  
• - Addresses the chaotic behavior of different attractors and their mathematical expressions. Includes plots, images and program source codes.
  
• - Research group at the INRIA national research center, France. Includes research details, publications and software.
  
• - Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
  
• - Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
  
• - Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
  
• - Explains the basics. Includes gallery and free software for exploring different sets and singularities.
  
• - Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
  
• - Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
  
• - Images generated by different commercial applications. Includes FAQs and tutorial.
  
• - Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
  
• - Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references.
  
• - Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact.
  
• - Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
  
• - Comprehensive tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
  
• - Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.
  
• - Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
  
• - 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.
  
• - Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
  
• - Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
  
• - Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
  
• - Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
  
• - Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
  
• - Index and definition of different attractors. Includes images, plots and glossary.
  
• - Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
  
• - Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets.
  
• - Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.
  
• - Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.
  
• - Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
  
• - Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references.
  
• - Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
  
• - Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.
  
• - Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references.