Brownian motion
Fractals in Physics

Brownian motion has a long history, dating back to its systematic study by R. Brown in the 1830s. Using a microscope, this botanist noticed that tiny plant spores suspended in water moved endlessly in apparently disordered, aimless motions. The first hypothesis of the biological origin of these movements was quickly discarded when he realized that the same kind of agitation could be seen in small mineral particles. What remained was the explanation that this movement was due to water itself. Indeed, changing the composition of the liquid, as well as its temperature, can vary the properties of this movement.

It took three quarters of a century for a reasonable explanation...