Programming Sampler

Examples of small programs written in the Mathematica language.

Difference Tables

Definition

Example

Gray Code

Definition

Example

Mandelbrot and Julia Sets

This creates a compiled function which computes membership in the Mandelbrot set.

This generates a density plot using the function.

Here is a compiled function that computes membership in a Julia set.

This generates a picture of an array of Julia sets.

Game of Life

Direct definition, operating on an array of black and white squares

Optimized definition, operating on a list of positions of black squares

Here are the initial coordinates of the glider gun structure

This runs 10 steps in the evolution of the glider gun

This displays the evolution in 3D

Mellin Transforms

Definitions

Example

Integration over a Triangle

Definitions

Example

Weights for Finite Differences

Definitions

Example: computing the weights for a 9-node second derivative symmetric approximation