#### Random Walk in 2D

Visualization to illustrate the crazy fact that a random walk on the integer lattice in dimension d <= 2 will return to its starting point with probability 1 whereas a random walk in dimension d >= 3 has a finite probability of never returning. Or in other words:

"A drunk man will find his way home, but a drunk bird may get lost forever." - Shizuo Kakutani

Click here for a [random walk in 3D](http://bl.ocks.org/EmilienDupont/7cd47996390fe5b3b91481b823348bbc).

For a cool proof of this theorem using Fourier analysis check e.g. the [Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf).