The Lakes of Wada partitions the unit square in to three regions, all of whom share a common boundary. The Wikipedia entry (http://en.wikipedia.org/wiki/Lakes_of_Wada) gives a construction approach, and a picture of a first few steps of the construction.

Is there a good algorithm available somewhere to explicitly list the partition up to some specific iteration? Or a closed form expression for the boundary in the limit of the process?

I'm hoping for something I can implement myself, or a piece of software that already does it, and in the end get a picture to arbitrary high levels of detail and arbitrary high iterations of the construction.