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Models of Morphogenesis

Models of Morphogenesis. Radhika Nagpal. Outline. Cellular Automata Reaction-Diffusion Models DLAs L-Systems. Cellular Automata. Stylized/Discrete Dynamical Systems Ulam and von Neumann, 1940s Self-reproducing machines. Conway’s Game of Life. Models of Natural Systems.

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Models of Morphogenesis

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  1. Models of Morphogenesis Radhika Nagpal

  2. Outline • Cellular Automata • Reaction-Diffusion Models • DLAs • L-Systems

  3. Cellular Automata • Stylized/Discrete Dynamical Systems • Ulam and von Neumann, 1940s • Self-reproducing machines

  4. Conway’s Game of Life

  5. Models of Natural Systems • Lattice Gas models • Social Insect models • Traffic Models, Epidemic Spread • Evolutionary models

  6. Chemical PatternsReaction Diffusion Models [Turing, 1952]

  7. Gray-Scott Model

  8. Parameter Space

  9. Activator-Inhibitor Model(Grierer and Meinhardt) • Key: Local self-enhancement, Long range Inhibition

  10. Examples • Belousov-Zhabotinsky Reaction (BZR) • AngleFish Stripe formation • Symmetry-breaking (Budding Yeast)

  11. Crystal GrowthDiffusion-limited Aggregation (DLA)

  12. Branching PatternsL-systems and Grammar Rules

  13. Types of Rules/Structures • Lineage (Context free) • Context sensitive (Information flow) • Environmentally-sensitive • Phyllotaxis • Good match for describing the spatial-temporal patterns of plants

  14. Sources of Images and Movies: • Images and Movies for DLAs and L-systems: Visual Models of Morphogenesis: A Guided Tour by Prusinkiewicz, Hammel, and Mech (http://www.cpsc.ucalgary.ca/Research/bmv/vmm-deluxe/) • Reaction Diffusion Movie: Amorphous Computing Website • Snowflake Images: Rasmussen & Libbrecht Collection (http://snowflake.com/) • Game of Life: movie from Georgia Tech Altera Page (http://users.ece.gatech.edu/~hamblen/ALTERA/altera.htm)

  15. Extra slides

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