diffusion
Mathematical Programming with Python
https://people.sc.fsu.edu/~jburkardt/classes/...
python_2025/diffusion/diffusion.html

diffusion: Brownian motion, random walks, diffusion, the heat equation; estimating the mean distance of a random walker from the origin after a certain number of steps. Plotting random walks in 1D, 2D, or 3D. Computing a random direction in 3D using normal random numbers.

Lecture notes:

• diffusion.pdf

• percolation.py, the percolation model, after the component calculation was corrected.
• components.png

• motion_1d.py, model the motion of a single Brownian particle over many steps in 1D.
• motion_1d.png
• motion_2d.py, model the motion of a single Brownian particle over many steps in 2D.
• motion_2d.png
• motion_3d.py, model the motion of a single Brownian particle over many steps in 3D.
• motion_3d.png

• walk_1d.py, on average, how many unit steps before a Brownian particle in 1D is L units away?
• walk_1d.png,
• walk_2d.py, on average, how many unit steps before a Brownian particle in 2D is L units away?
• walk_2d.png,
• walk_3d.py, on average, how many unit steps before a Brownian particle in 3D is L units away?
• walk_3d.png,

• scatter_1d.py, release many Brownian particles in 1D at once. How will they scatter over the region after 100 steps?
• scatter_1d.png,
• scatter_2d.py, release many Brownian particles in 2D at once. How will they scatter over the region after 100 steps?
• scatter_2d.png,
• scatter_3d.py, release many Brownian particles in 3D at once. How will they scatter over the region after 100 steps?
• scatter_3d.png,