Fractals

Self-similarity and infinite complexity at every scale - from coastlines to the Mandelbrot set

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How Long is Britain's Coastline?

A simple question with an impossible answer...

In 1967, mathematician Benoit Mandelbrot asked this question and discovered something that changed geometry forever.

The Coastline Paradox

Try measuring Britain's coastline with different sized rulers. As your ruler gets smaller, you can measure more detail - every bay, every inlet, every rock.

Your Measuring Ruler: 100 km

600

kilometers measured

60

ruler lengths used

Coastline Detail at 100km Resolution

Notice something strange? The smaller your ruler, the longer the coastline becomes! Try moving the slider from 200km down to 10km. What happens to the measured length?

Try it! Move the ruler slider to see how the measured coastline length changes. What happens as you use a smaller and smaller ruler?

The Wild

The Wild

The Wild

The Wild

Fractals

Self-similarity and infinite complexity at every scale - from coastlines to the Mandelbrot set

How Long is Britain's Coastline?

A simple question with an impossible answer...

The Coastline Paradox

Your Measuring Ruler: 100 km

600

kilometers measured

60

ruler lengths used

Coastline Detail at 100km Resolution

Fractals

Self-similarity and infinite complexity at every scale - from coastlines to the Mandelbrot set

How Long is Britain's Coastline?

A simple question with an impossible answer...

The Coastline Paradox

Your Measuring Ruler: 100 km

600

kilometers measured

60

ruler lengths used

Coastline Detail at 100km Resolution