8. Recursion: Fractals, Chaos and Dynamic Systems


A single mathematical technique, that of recursion, where the results of one iteration of a function are fed back into the function, gives rise to a wealth of modeling techniques for exploring natural forms and processes.

Reading
In James Gleick, Chaos, Making a New Science (1987), ch 1, pages 11-31, "The Butterfly Effect"; ch 3, pages 57-80, "Life's Ups and Downs"; ch 6, pages 155-187, "Universality." Personal copy on reserve at the Flaxman Library.
Edward Lorenz, The Butterfly Effect, PDF of a famous lecture, from Lorenz, The Essence of Chaos.
Edward Lorenz, note on the Logistic Equation, from The Essence of Chaos.
Suggested supplemental reading: Benoit Mandelbrot, The Fractal Geometry of Nature (1982), Heinz-Otto Peitgen and Peter Richter, The Beauty of Fractals (1986), both in Flaxman Library. Also, Heinz-Otto Peitgen and Dietmar Saupe, The Science of Fractal Images (1988), a more technical text.

Assignment
Use the output from a dynamic system to produce an image, animation or time-based performance.

Code
Dynamic Systems, incuding FigTree and ThreeAunts. FigTree requires Andreas Schlegel's ControlP5 library for Processing.
Daniel Shiffman's sample code for Fractals and Cellular Automata.
Also let me call your attention to updates to Steering techniques (boids): TurtleBoid Sandbox 2 and Torus Mapping.

Assignment
Use the output from a dynamic system to produce an image, animation or time-based performance.
OR Photographic images, video, drawings: collect a personal gallery of fractal images.