Click the board to drop an 'Ant'.
The Ant will randomly go one step at a time in one of the four orthogonal directions. A colour scheme shows how often a psoition is revisited by the Ant. After twenty visits the colour scheme repeats.

Before you start, you can draw walls to limit the movements of the Ant. Click one of the option buttons POINT, LINE and SQUARE for this first. After the drawing, click the READY button before you drop the Ant.

Note that there are alternative boards and alternative colour schemes available (hit 'switch piece set' button repeatedly).

There is no win message.

 
Random walks are an interesting subject in science. I have never seen anything published on the many interesting RESTRICTED walks (no forward moves etc) as given in the variants of this game. There might be new things to be discovered...?
Also, the confinement to a finite board is interesting:
What is the most probable number of moves after which the n x n - board is filled?
Are the fractal dimensions of the areas visited different in each case?
Which variant fills the board the fastest?

Three-dimensional random walks are closely related to the statistical jostling of ('Brownian Motion') of molecules in three dimensions. In this game we only look at two-dimensional walks, however.

More freeware and real puzzles and games at my homepage: karl.kiwi.gen.nz.