# Why Are Lightning Bolts Fractal?

Question sent by JOSE GALÁN (Alacant). EDUARDO ROS answers:

«Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel a straight line» are Benoît Mandelbrot’s genius opening lines for his book The Fractal Geometry of Nature. Mandelbrot enunciated the concept of fractal taking other scientists’ intuitions as a starting point. If we chop a cauliflower we can see that in every piece we find what looks like a smaller cauliflower. A piece of cloud looks like a small cloud and a mountains’ peak looks like a small hill. This phenomenon is known as self-similarity (the whole has the same shape as one or more or the parts).

Just as we can represent a pine tree by showing one of its branches (in Christmas decorations, for example), if we look carefully at one part of the lightning bolt, its appearance is exactly the same as the whole lightning. From this perspective, lightning bolts are fractal. Lightning bolts occur when the amount of electrical charge in the atmosphere overcomes the air’s insulating properties. This overcoming is a kind of momentary «crack» that breaks through the air charged with electricity. This fracture can be compared to the water that makes its way down a mountain or to a tree’s roots or branches. In this process small electric fractal «cracks» form in the air.

What is more, when we talk about fractals we can talk about «intermediate» dimensions. A straight line has dimension 1, a plane has dimension 2, and a cube dimension 3. A fractal object sssssses lightning travel , ractals we can talk about «intermidiate»s exactly the same example) nor does lightning travel «fills» space in such a way that it is not within a whole dimension, but a dimension with decimals. Just as we could say that the fractal dimension of a broccoli is 2.66, a lightening’s approximate fractal dimension is 1.5. This number is greater than 1, which indicates that a lightning bolt trajectory fills more space than an ordinary curve.

Eduardo Ros. Director of the Observatori Astronòmic de la Universitat de València.