Chaos Under Control Sample Syllabus 4

David Peak and Michael Frame

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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