#### Write4U

**Valued Senior Member**

Yes, those are the human mathematics which are symbolized abstractions of functional universal natural mathematics.A very large amount of mathematics is not derived from the observation of nature. It is pure concept, built out of abstract axioms and such. "Derived" is also a terrible word to use, there. When a mathematician derives a mathematical proof, she does not pay any attention to observations of nature. That would be science, not maths.

But this also demonstrates the infinitely possible applications of mathematics, definable both in terms of implicated potentials or as expressed physics. I bet

*universal functions*use fairly simple mathematics (constants) but at cosmic scales.

### chaos theory

**mathematics and mechanics**

In classical mechanics the behaviour of a dynamical system can be described geometrically as motion on an “attractor.” The mathematics of classical mechanics effectively recognized three types of attractor: single points (characterizing steady states), closed loops (periodic cycles), and tori (combinations of several cycles).

In the 1960s a new class of “strange attractors” was discovered by the American mathematician Stephen Smale. On strange attractors the dynamics is chaotic. Later it was recognized that strange attractors have detailed structure on all scales of magnification; a direct result of this recognition was the development of the concept of the fractal (a class of complex geometric shapes that commonly exhibit the property of self-similarity), which led in turn to remarkable developments in computer graphics.

More From Britannica

principles of physical science: Chaos

Applications of the mathematics of chaos are highly diverse, including the study of turbulent flow of fluids, irregularities in heartbeat, population dynamics, chemical reactions, plasma physics, and the motion of groups and clusters of stars.

### Chaos theory | Definition, Examples, & Facts | Britannica

Chaos theory, in mechanics and mathematics, the study of apparently random or unpredictable behavior in systems governed by deterministic laws. Applications of the mathematics of chaos are highly diverse, including the study of turbulence, heart irregularities, plasma physics, and the motion of...

www.britannica.com

**But why and how do regular patterns form within chaos? What are the guiding equations that cause similar patterns to form with regularity?**