#### Custom Maze Solver (JavaScript, PHP)

Allows the user to upload an image of a maze (or choose a premade one), then finds a shortest (Manhattan) pixel path between two chosen points by using Dijkstra’s algorithm.

#### Markov Chain Text Generator (JavaScript)

Lets the user enter a sample text, then generates text that is similar to it by using a Markov chain.

#### 3D Wireframe Engine (Java)

A simple 3D engine that uses the drawLine() method from the Java Graphics library and Euler angles to render an interactive wireframe environment from scratch. Use the arrow keys and QWEASD to navigate.

#### Wolfram Spiral Automaton (JavaScript)

A cellular automaton inspired by Stephen Wolfram’s elementary cellular automaton rules. Here, the the cell wanders outward in a counterclockwise spiral in an infinite square grid. For each step, its color (among three possibilities, by default) is determined by the colors of its eight adjacent cells. The rule (which is displayed by setting verbose=true in the URL) for how coloring is performed is randomized by default, but can be specified in the URL via the parameter *rule* (i.e. append &rule=3c… to the URL). Here is a gallery of some generated images.

#### Julia Set Randomizer (PHP)

Draws a random Julia set as a PNG image with the GD Graphics Library. The URL parameters *width* and *height* can be used to specify the image dimensions in pixels. The escape time algorithm is used for coloring. You can also look at the source code, or generate multiple Julia sets simultaneously.

#### Polynomial Shadow (Mathematica)

Takes a univariate polynomial *P* and plots shadow(*P*,*n*), i.e. the union of all zeros of all orders of the derivative of *Pⁿ*, where *n* is a fixed natural number. In the plot, the large dots and squares are the zeros and critical points of *P*, respectively, the triangle is the center of mass of the zeros of *P*, and the small squares are the branch points of equations (1.3) and (1.4) in the *z*-plane from my paper that the program is based on. Here is the code in text format, and here is a gallery of some shadows.