Doodling and maths: A matter of black and white

21 Nov 2016

Maths and doodling. Image: Syda Productions/Shutterstock

Maths has myriad applications, but did you know how instrumental it can be in the complicated world of doodling?

Last week, we were introduced to Quick, Draw!, a Google-backed artificial intelligence (AI) experiment that engages in machine learning by analysing your sub-par doodling skills.

That’s cool and all, but there’s much more to doodling than simple AI-training fodder – it’s a mathematical dream.

Let’s look at James. After trying in vain to solve his maths homework for the next day, a very tired James starts to doodle meaningless patterns on the side of his sheet.

While doodling, James follows some simple rules:

  1. Once started, he doesn’t lift the pen off the paper
  2. He finishes at the exact point where he started
  3. Most importantly, he is unable to retrace his steps back over a piece of curve already drawn

The result is a curve with several self-intersections, like this:

Maths doodle

This curve divides the plane in several regions.

Now James wants to do some colouring (anything to avoid that maths homework). He colours some of the regions black and leaves others white, so that no regions sharing a length of border are of the same colour. You can see his work above.

But, can James always do the same with any other doodle obeying the same simple rules?

This problem was suggested by Mayya Golitsyna, PhD student in the School of Mathematics and Statistics, University College Dublin (UCD), who is actively involved in the UCD Mathematics Enrichment Programme and the Irish Mathematical Olympiad.

Want stories like this and more direct to your inbox? Sign up for Tech Trends, Silicon Republic’s weekly digest of need-to-know tech news.

Kirsty Tobin was careers editor at Silicon Republic