The mathematics of nature.
Excerpt from the book “The fractal objects” by Benoît Mandelbrot (1975) read in the film:
Flows in fluids are multidimensional phenomena, the three components of velocity being functions of the three coordinates of space and time, but the empirical study so far has had to pass through one or more one-dimensional “slices”, each of which constitutes the chronicle of one of the velocity coordinates, at a fixed point. To get an intuitive idea of the structure of the cut through an atmospheric mass moving in front of the instrument, let us reverse the roles and take as “instrument” an airplane. A very rough level of analysis is illustrated by a very large airplane. Some corners of the atmosphere obviously appear to be turbulent, with the plane being shaken. In contrast, the rest appears laminar. But let’s do the test again with a smaller plane: on the one hand, it “feels” turbulent gusts where the big one didn’t, and on the other hand, it breaks down each shake of the big one into a gust of weaker shakes. So, if a turbulent piece of the section is examined in detail, it reveals laminar insertions, and so on as the analysis is refined, until the viscosity interrupts the cascade.