Fractals: Nature's Numbers?

by Daryl Hepting

Can numbers describe nature?

Finding numbers to describe nature can bring to it a sense of order. Some examples from history include:

Can numbers describe coastlines or clouds?

Fractal dimension

Look at this progression of shapes. Can you see a pattern?

Think of the original line in 3 segments. Replace those 3 segments with 4 segments, as shown in the second curve. Repeat.

The dimension of this curve: log4 / log 3.

Nature's dynamics

The natural world is filled with dynamic processes:

Forgeries or the real thing?

Mandelbrot, the father of fractal geometry once said:

clouds are not spheres,
mountains are not cones,
coastlines are not circles,
and bark is not smooth,
nor does lightning travel in a straight line ...

Can you see any similarities between these following two video clips?