Fractal Geometry, Probability and Chaos Lesson

This lesson demonstrates the surprising fact that a chaotic and unpredictable process can lead to an ordered, predictable outcome, throwing in concepts and calculations from probabilities and geometry. It can be a great contrast to sequences and series, where they use a repetitive nth term rule to get an ordered list.

The resource contains a word document that will lead students through the Chaos Game (consider keeping page 2 for yourself and talking through it!). It has simple rules but plenty of interesting discussion points around probability. Having seen this unique fractal arising from an unpredictable process, they can explore how and why it happens before moving onto the powerpoint about fractals in nature. The slides also lead them through the surprisingly simple proof that a Koch snowflake (another fractal!) has infinite perimeter and yet finite area - all they need is knowledge of fractions. It’s an enrichment lesson designed to engage the students and give them pride in the amazing things they can prove!

This lesson is suitable for most secondary school classes.