MAT 200C: Pattern Formation
Spring 2014
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All topics and dates are tentative
Date
Topic
Supplemental Materials
Conway's Game of Life
Link:
Wikipedia
Link:
Original Scientific American article
The Mandelbrot Set
Link:
Wikipedia
Link:
Wikipedia, Julia Sets
Link:
The Fractal Geometry of Nature
Mandelbrot Potential
Link:
Exploring the Mandelbrot Set
Link:
Coloring Dynamical Systems in the Complex Plane
Link:
Ray Tracing Deterministic 3-D Fractals
Link:
Wikipedia, Buddhabrot
Link:
Wikipedia, Mandelbulb
Newton fractals
Link:
Wikipedia
- Newton fractals
Link:
Wikipedia
- Newton-Raphson iteration
Diffusion Limited Aggregation
Link:
Wikipedia
Link:
Original Physical Review Letters article
Link:
The Dielectric Breakdown Model
Link:
The conformal mapping method
Link:
The potential distribution around growing fractal clusters
Link:
My version
Finite Differences - Gradients
Link:
Wikipedia
Link:
Mathworld
The Heat Equation
Link:
Wikipedia - the heat equation
Link:
Wikipedia - the Laplacian
Link:
Wikipedia - the CFL condition
Reaction-Diffusion
Link:
Wikipedia
Link:
Turing's original article
, "The Chemical Basis of Morphogenesis"
Link:
Turing patterns in the laboratory
Link:
Greg Turk's version
Link:
Witkin and Kass' version
Link:
My version
Link:
The "Turing Test" paper
Book:
Alan Turing: The Enigma
Book:
A Madman Dreams of Turing Machines
The Wave Equation
Link:
Wikipedia
Link:
Simulating Ocean Water
Link:
A Numerically Efficient and Stable Algorithm for Animating Water Waves
Link:
Rapid, stable fluid dynamics for computer graphics
Vibration
Link:
Wikipedia - Vibration
Link:
Wikipedia - Can One Hear the Shape of a Drum?
Link:
Can One Hear the Shape of a Drum?
Book:
Theory of Vibration
Noise
Link:
Perlin's original article
Link:
Improving noise
Link:
Wavelet noise
Link:
Procedural noise using sparse Gabor convolution
Link:
Anisotropic noise
(the one we implement)
Scalar Turbulence
Link:
Perlin's original article
Link:
Improving noise
Link:
Wavelet noise
Link:
Procedural noise using sparse Gabor convolution
Link:
Anisotropic noise
(the one we implement)
Incompressibility
Link:
Curl Noise
Link:
Wavelet Turbulence
Link:
Evolving sub-grid turbulence for smoke animation
Link:
Fast animation of turbulence using energy transport and procedural synthesis
Sound
Link:
FoleyAutomatic: physically-based sound effects for interactive simulation and animation
Link:
Synthesizing sounds from rigid-body simulations
Book:
Real Sound Synthesis for Interactive Applications
Final Presentations