Happy Holidays from ThinkTank Maths - 2008

20 December 2008

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The pattern you see is generated by little creatures called Langton ants, originally invented by Christopher Langton, one of the founders of the field known as artificial life. The letters of your name encode the starting positions of three ants, who then weave their trails together to produce a unique pattern.

You can use the form to create patterns for your friends. Clicking on the image will give you a large version that you can print out and use as wrapping paper. An A4 sheet should be just the right size for a small meaningful gift!

Alternative Colours:

A Langton ant is a very simple critter: it starts out by heading in a selected direction and looks at the colour of the square it lands on. If the ant lands on a coloured square, it paints it white and turns 90 degrees to the left. If it lands on a white square, it paints it with its colour and turns 90 degrees to the right.

Although the rule is very simple, a Langton ant can generate quite complex behaviour. Initially it behaves very chaotically. But after a while it may shoot off in one particular direction, as if it has suddenly decided what to do — building a diagonal band structure called a “highway”.

One of the biggest unsolved mysteries about Langton ants is that they always seem to create a highway, even if their surroundings are initially peppered with black squares. But no mathematical proof that this always happens exists!

Langton’s ants illustrate the idea that simple mathematical rules can underlie complex behaviour in nature. Especially in the middle of the stressful holiday period, it is good to keep in mind that beauty can often be found in simplicity…

Explore other ThinkTank Maths seasonal greetings.

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