## More on Science4All

Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7) Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7)

By Lê Nguyên Hoang | **Updated:**2016-02 | **Views**: 0

Mathematical Physics, Determinism, Game of Life (Hiking in Modern Math 6/7) Mathematical Physics, Determinism, Game of Life (Hiking in Modern Math 6/7)

By Lê Nguyên Hoang | **Updated:**2016-03 | **Views**: 0

Dynamics, Chaos, Fractals (pt 1) Dynamics, Chaos, Fractals (pt 1)

By Scott McKinney | **Updated:**2016-02 | **Views**: 4546

The study of dynamical systems, natural or abstract systems that evolve at each instance in time according to a specific rule, is an active and fruitful area of research in mathematics. Its study has yielded insights into the nature of social networks such as Facebook, the spread of diseases such as influenza, and the behavior of the financial markets. In this series of posts, we'll look in depth at dynamical systems, as well as at the related subjects of chaos theory and fractals, all of which are both interesting and useful for understanding our world.

Dynamics, Chaos, Fractals (pt 2) Dynamics, Chaos, Fractals (pt 2)

By Scott McKinney | **Updated:**2015-12 | **Views**: 2140

Dynamical systems such as a system of 3 planetary bodies can exhibit surprisingly complicated behavior. If the initial state of the system is slightly varied, the resulting system behaves in a radically different manner. This "sensitivity to initial conditions" is a key element of what's become (perhaps disproportionately) well-known as chaos. Using the mathematical notion of iterative systems, we can model such systems and understand how chaos arises out of deceptively simple foundations.