This material is from the Winter 2014 offering of PMATH 370, and is for reference only.

JAVA APPLETS for Chaos and Fractals

REAL QUADRATIC MAP APPLETS

Nonlinear Web applet [Boston University] displays the cobweb diagrams for a variety of functions, including cosine, quadratic and tent maps.

Chaos Lab [University of Bremen] displays the time series, cobweb, frequency and bifurcation diagrams for a variety of functions, including cosine, logistic and tent maps.

Cobweb diagrams for f(x) = x^2 + c [Evgeny Demidov] Shows repelling fixed points and attractive cycles.

Iteration of the Logistic Map [Andy Burbanks]

The Period-Doubling Route [Washington State Univerisity] Zoom in on the bifurcation diagram.

Lyapunov exponents, bifurcation diagrams and other applets. [Brian Davies]

LORENZ ATTRACTOR APPLETS

Lorenz attractor. [Paul Falstad] Good animation; can enlarge and rotate in 3D. Also general 2D vector fields.

Lorenz Attractor [Michael Cross] Best applet. Can enlarge. The two orbits track each other for a considerable time.

Lorenz Butterfly [Exploratorium] Neat; click twice for sensitive dependence on initial conditions

Lorenz attractor Applet [SeigoNakamura] Neat and simple.

Lorenz attractor Applet [Patrick Worfolk]

HENON MAP APPLETS

Henon Map [Michael Cross] Can enlarge. Slow the Speed. To show orbit of one point, Set Points=1, Mark=1.

Henon Map with the bifurcation diagram [Arizona State University]

Henon Map with additional information

DOUBLE PENDULUM APPLETS

The Double Pendulum [Northwestern University] Good demo.

Two Double Pendulums [Rocky Jones and Kush Patel] Shows sensitive dependence.

FRACTAL APPLETS

Fractal landscapes, L-systems (plants + space-filling curves) [Dennis Rapaport] Lots of good demos.

FRACTAL DIMENSION

Coastline of Hong Kong. [Chi Tse]

Henon map, Circle map and Sinai Map [Michael Cross] Calculate fractal dimensions. (Equations for the maps)

Fractal mountains [Matthew Caryl]

MANDELBROT AND JULIA SETS

Big Mandelbrot set. [Evgeny Demidov]

Mandelbrot set and Julia sets. [Evgeny Demidov]

Julia orbit trip. [Evgeny Demidov]

The Fractal Microscope

Mandelbrot and Julia sets [Boston University]

Java Julia set generator [Mark McClure]

Or use a non-web program for your type of computer

XaoS real-time interactive fractal zoomer for various platforms [Thomas Marsh and Jan Hubicka]

Fractint for PCs

Dynamics [Richard Koch and Pierre d'Herbemont] for Mac OS X

ITERATED FUNCTION SYSTEMS

Iterated Function System [Noah Goodman]

Chaos Game - Sierpinski Gasket [Shodor]

Classic Iterated Function Systems [Larry Riddle]

FRACTAL IMAGE COMPRESSION

Fractal Image Compression [EURECOM]
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