Edit: I've responded to a few critiques below.
The Travelling salesman problem is stated as: "Given a number of cities and the costs of travelling from any city to any other city, what is the least-cost round-trip route that visits each city exactly once?"
I used the open source classes listed at the link below to create a Processing program that would solve the Travelling saleman problem using Genetic algorithms. Re-used paths (corresponding to Chromosomes) increase in visibility as they're re-used, fading otherwise, meaning the paths 'emerge' as certain chromosomes become more dominant.
The problem is considered 'solved' when a hundred generations have passed without a more optimal solution having been found.
I also made the problem 3D, simply because... well, everything looks nicer in 3D and, to be honest, it was incredibly easy to program, given the class I used from the link below. I would've made this a lot prettier but I'm running out of free/unemployed time as I start a new job soon, so I got it working and left it.
Updated: Hello Reddit and Wired. The simulation posted does not claim to be the 'perfect' solution for the layout shown. Running the program a number of times produces not only different 'solutions' but also a wide variation in the number of generations required to create a 'solution' - anything from 800 to 5000, depending entirely on the randomised initial population and their genetic makeup.
Genetic Algorithm classes: http://www.heatonresearch.com
Travelling Salesman: http://en.wikipedia.org/wiki/Traveling_salesman_problem