A primer on mathematics in the age of the computer

Julia and Mandelbrot Set Explorer David E. Joyce (djoyce@clarku.edu) For background on Julia and Mandelbrot sets, see the introduction. There is detailed help available for using this form. Mandelbrot Set: x in ; y in . Parameters Clicks on the Mandelbrot set image will get a Julia set magnify the Mandelbrot set by a factor of Alternate Mandelbrot parameter plane mu lambda (mu = ...

The Computational Beauty of Nature - Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation ...

CCSR Homepage ...

An interactive introduction for everyone to Chaos Physics and Chaotic Motion in Classical and Quantum Mechanics ...

Dancing Triangles The Dynamical Systems and Technology Project at Boston University Zooming Sierpinski This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. It ...

Newton Basins David E. Joyce (djoyce@clarku.edu) August, 1994 Table of contents Introduction (this is it) Background on Newton's method Some examples Generation form Technical details References in books and on the web Newton's method for finding solutions to equations leads to some fantastic images when it's applied to complex functions. You start with an initial guess for the solution which ...

Fractal Pages frac tal (fr k tel) n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature. Fractals are extensions of traditional Euclidean shapes, such as lines, squares, and circles, with two ...

Fractals and combinatorics diagrams created using Mathematica.

Cynthia Lanius Fractal Properties Fractional Dimension Table of Contents Introduction Why study fractals What's so hot about fractals, anyway Making fractals Sierpinski Triangle Using Java Math questions Sierpinski Meets Pascal Jurassic Park Fractal Using JAVA It grows complex Real first iteration Encoding the fractal World's Largest Koch Snowflake Using Java Infinite perimeter Finite area ...

This site helps those with different levels of computer experience to create fractal images and music. It includes a brief overview of selected software and on-line interactive sites, a program-related fractal gallery and links to selected educational tutorials and resources.

A java applet to discover regions of the Mandelbrot Set ...

Chaos Theory Chaos Theory The Division of Labour Chaos and Dialectics Dialectical materialism, elaborated by Karl Marx and Frederick Engels, was concerned with much more than political economy: it was a world view. Nature, as Engels in particular sought to demonstrate in his writings, is proof of the correctness of both materialism and dialectics. My recapitulation of mathematics and the ...

A guide to fractals and chaos for the beginner with a fractal art gallery.

IFS Attractors Recent changes 17th April 2002: added page for pseudo-terdragon. 18th April 2002: added page for m-pseudo-terdragons. 18th April 2002: added page for demi-pseudo-terdragons 18th April 2002: added page for m-demi-pseudo-terdragons 18th April 2002: added page for demi-m-demi-pseudo-terdragons 21st April 2002: added more octiamonds 22nd April 2002: updated reference to Karl Dahlke's ...

Fractal Map - A fun and addictive online fractal viewer. No Java required ...

Kleinian Groups Pictures This set of pages will eventually contain a collection of computer graphics connected with the mathematical theory of Kleinian Groups. We have currently available: Source Code for Programs This contains the source code for the FORTRAN programs used in this study, as well as some sample data files to be fed to this program. Study of a cross-section of the quasifuchsian ...

3D fractals with bicomlex dynamics! See the generalization of the Mandelbot set. See great and innovative 3D fractals renderings!

Introduction to Lacunarity Erik Rauch Also on fractals: A Fractal Brownian Archipelago Em Portugues Lacunarity is a counterpart to the fractal dimension that describes the texture of a fractal. It has to do with the size distribution of the holes. Roughly speaking, if a fractal has large gaps or holes, it has high lacunarity; on the other hand, if a fractal is almost translationally invariant, ...

A Directory of Internet resources on chaos theory and fractals.