Fractal Dimension

Between 1 and 2

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Dimension $D$: scaling by $s$ gives $N = s^D$ copies, so $D = \log N / \log s$.
• Sierpinski ≈ 1.585, Koch ≈ 1.262: fractals have non-whole dimensions.
• Coastlines, clouds and ferns are approximately fractal.

Steps

1. Scaling copies
2. Dimension from scaling
3. Koch dimension
4. Box counting
5. The Sierpinski carpet
6. How long is Britain’s coast?