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HONR 300/CMSC 491 Complexity

HONR 300/CMSC 491 Complexity. Prof. Marie desJardins, January 31, 2011. Course Topics. Reproduced from Gary Flake, The Computational Beauty of Nature , MIT Press, 1998. Topics. 1/26-2/9: 2/14-2/28: 3/2-3/9: 3/14: 3/16-3/30: 4/4-4/11: 4/13-4/20: 4/25-5/11:.

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HONR 300/CMSC 491 Complexity

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  1. HONR 300/CMSC 491Complexity Prof. Marie desJardins, January 31, 2011

  2. Course Topics

  3. Reproduced from Gary Flake, The Computational Beauty of Nature, MIT Press, 1998

  4. Topics • 1/26-2/9: • 2/14-2/28: • 3/2-3/9: • 3/14: • 3/16-3/30: • 4/4-4/11: • 4/13-4/20: • 4/25-5/11: Complexity, mathematical and algorithmic background Fractals Chaos Midterm Cellular and finite-state automata (machines) Multi-agent systems Optimization and adaptation Presentations, classifier systems, additional topics

  5. Sources of Complexity

  6. Complexity and Agents • Complexity in systems arises from interactionsbetween individual components or agentsof the system • Emergenceis the concept that system behavior is not readily inferred from individual agent behaviors: it arises from the interactions between the agents in complex and beautiful ways • Self-similarity arises when similar patterns occur at multiple levels of abstraction or multiple parts of a system • Sources of complexity: • Parallelism • Recursion • Adaptation

  7. Parallelism michaelmcfadyenscuba.info/ reference.findtarget.com mathaware.org http://hermetic.ch/

  8. Parallelism • Parallelism: Many copies of identical or highly similar agents operating simultaneously (but potentially interacting with each other) • Examples: • Biological/biochemical systems: Fish schools, ant colonies, protein folding • Mathematical models: Cellular automata • Physical processes: Galaxy formation, planetary rings • Social/technological systems: Economic markets, social networks, structure of the Internet, RAID disk arrays

  9. Recursion faqs.org wikipedia.org condostx.com wallpaperstock.net

  10. Recursion • Recursion: a repetitive process in which a process is invoked repeatedly on successively smaller versions of the entity or problem being manipulated • Examples of recursion: • Biological processes: Tree branches, seashells, coral reefs • Mathematical models: Fractals, L-systems • Physical processes: Coastal formation, sand dunes, snowflakes, cloud formations, mountain ranges • Social systems: Micromarkets, hierarchical organizations, clan systems, governmental systems, knowledge structures

  11. Adaptation intranet.friaryschool.net pinnycohen.com mms.nps.gov scienceray.com childrenshospital.org

  12. Adaptation • Adaptation: Modification of an agent or a species (collection of agents over time, through reproduction) in response to environmental pressures (competition for resources) • Examples: • Biological systems: Evolution, drug-resistant bacteria, learning and memory, cancer • Mathematical models: Dynamic optimization, feedback models • Physical processes: Global climate change, meandering river shapes, mineral formation • Social systems: Opinion formation, market fads, competitive markets, social protocols/etiquette

  13. Self-Organization Let’s Play!

  14. How Big is a Complex System? • Powers of Ten movie: http://www.powersof10.com/film • Scale of the Universe animation: http://primaxstudio.com/stuff/scale_of_universe/

  15. What Next? • Reminder: The “Complexity in Everyday Life” assignment is due this Wednesday, February 2.

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