1. Overview of fractals, chaos, and complexity (3 sessions, read Chs. 1 and 10)
* Quick introductions to self-similarity, chaos, and self-organization
2. Self-similarity and iterative processing (3 sessions, read Ch 3)
* examples from Nature, art, music, and poetry
(Lab: analysis of fractal aspects of poetry, including creating some)
3. Fractal dimensions (3 sessions, read Ch 3)
* dimension as exponent
* information contained in dimension
(Labs: dimensions of paper wads, grain clusters, tear paths, and viscous fingers)
4. Dynamics: linear and nonlinear (6 sessions, read Ch 4)
* what a model is and what it isn't
* exponential growth and decay in linear dynamics
* the tent map
* the characteristics of chaos
* the Butterfly Effect
(Labs: properties of the simple pendulum; exponential growth)
5. Chaos, the arts, and the humanities (3 sessions, read appro. secs. of Ch 6)
* the Tent Map and the Myth of Sisyphus
* chaos and esthetics: a balance of surprise and regularity
* chaos and art: the work of Ellsworth Kelly
* chaos and music: constructing music from noises
* chaos and deconstruction
* chaos and history
* philosophical issues raised by chaos
(Lab: creating [music, art, poetry, ...] with chaos)
6. Controlling chaos (3 sessions, read approp. secs. of Ch 6)
* controlling the Tent Map
* controlling higher dimensional chaos: magnetic ribbons, lasers, electronic circuits, chemical reactions, flames, hearts, and brains; communications
* synchronization of chaotic systems: encoding communications
7. Cellular Automata (9 sessions, read Ch 9)
* cellular automata as models for physical, biological, and social phenomena
* 1- and 2-dimensional binary cellular automata
* the effects of boundaries
* Conway's Game of Life: gliders and other complex structures; Life as a universal computer
* Wolfram's classification scheme: examples in 1- and 2-d; Langton's order parameter
(Lab: CA exploration)
8. Self-organization (3 sessions, read Ch 9)
* self-organized criticality (SOC)
* SOC in Life, sandpiles, earthquakes, and the stock market
* how SOC amplifies external stimuli
* 1/f noise, SOC, and neuronal esthetics
(Lab: avalanches in grain piles)
9. Neural networks (3 sessions, read Ch 9)
* computation by a cellular automaton
* supervised learning: the backpropagation algorithm
* emergent properties and the amazing leap to generalization
(Lab: training a backprop network)
10. Complex adaptive systems (3 sessions, read Ch 9)
* flocking (schooling) behavior in artificial birds (fish)
* genetic algorithms: survival of the fittest
* defined fitness versus coevolution
* coevolutionary forces: emergent behavior in Ray's Tierra,Holland's Echo, Arthur's artificial economy, modern business organizations
11. Project reports by students (3 sessions)
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