Hope the video is fun, and here’s a math puzzle I thought of while creating it.

The algorithm:

Pen width = 12px Canvas x bounds = [-900px, 900px] Canvas y bounds = [-600px, 600px]

At each timestep: - The pen starts at the origin - A direction is chosen [N,S,E,W] with each direction receiving 25% probability. - The pen moves forward in that direction with a distance chosen uniformly from the integer range [50,75] - After moving, if the pen is out of bounds of the canvas in the x direction, set its x coordinate to 0 leaving the y coordinate unchanged - After moving, if the pen is out of bounds of the canvas in the y direction, set its y coordinate to 0 leaving the x coordinate unchanged

What is the probability that at timestep t, a pixel (x, y) is colored?