# The Travelling Salesman Portrait

The Travelling Salesman Portrait Source – Fronkonstin.com

I have noticed even people who claim everything is predestined, and that we can do nothing to change it, look before they cross the road (Stephen Hawking)

Imagine a salesman and a set of cities. The salesman has to visit each one of the cities starting from a certain one and returning to the same city. The challenge is finding the route which minimizes the total length of the trip. This is the Travelling Salesman Problem (TSP): one of the most profoundly studied *questions* in computational mathematics. Since you can find a huge amount of articles about the TSP in the Internet, I will not give more details about it here.

In this experiment I apply an heuristic algorithm to solve the TSP to *draw* a portrait. The idea is pretty simple:

- Load a photo
- Convert it to black and white
- Choose a sample of
*black*points - Solve the TSP to calculate a route among the points
- Plot the route

The result is a *single line drawing* of the image that you loaded. To solve the TSP I used the arbitrary insertion heuristic algorithm (Rosenkrantz et al. 1977), which is quite efficient.

To illustrate the idea, I have used again this image of Frankenstein (I used it before in this other experiment). This is the result:

You can find the code here.