The geometry of chaos and the dynamics of fractals.

An enigmatic title, a phrase that represents a sort of two-faced palindrome, conceptually not literally, because it wants to highlight the duality between the fractals and the deterministic chaos. Once again I quote from a famous mathematician:

Following the mathematics practice and representing the dynamics in geometrical terms, one can well focus the disconcerting dual nature of chaos.
Associated with each dynamic system, there is its own geometric space, the phase space [...]. In chaotic systems the lines of flow (or state trajectories), head towards complex forms such attractors. [...] The geometry of these attractors combines the concept of chaos and the concept of fractal.

Ian Stewart - What shape is a snow flake? (translated from Italian).

The mathematics of chaos and fractal geometry are fundamental discoveries of the twentieth century, which allowed the review of basic concepts of many branches of science - not to say all the knowledge - much to be presented today as the ignition spark of a revolution epistemological still underway, whose significance is still difficult to understand.
Concepts such as chaos and fractal, abstruse to the most today, should become a basis for anyone who wants a key to our fascinating universe.