Simulating Reaction Diffusion Textures Using Turing's Equations

• Ashley Mascareno
• Is it possible to that certain well-known physical laws (reaction-diffusion equations) are sufficient to account for "complex" textures and patterns in nature?

Approach

Solve Turing's reaction-diffusion equations (partial differential):

• discretize Turing equations
• use a time-stepping algorithm
• solve with various values for rates and strength of interactions

Objectives

1. determine appropriate initial and boundary conditions
2. discretize Turing equations
3. estimate sensible parameters for rates and interaction strengths
4. solve equations with varying parameter sets to obtain patterns such as
   • stripes
   • spots
   • rings (extra)
   • "giraffe-esque" (extra)