First day was Topology, now it is the time for Chaos Theory. Hope you are enjoying the event as much as I do. Keep yourself curious and chaotic for today:
Chaos theory is the field of study in mathematics that studies the behavior and condition of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.
The history of Chaos theory is embedded in physics and computer science. An early proponent of chaos theory was Henri Poincaré. In the 1880s, while studying the three-body problem, he found that there can be orbits that are nonperiodic, and yet not forever increasing nor approaching a fixed point. In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature. Early studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident to some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments.
The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these systems.
Fractal theory is a big part of chaos theory and everything started in 1963 with Benoit Mandelbrot.
Chaotic behavior exists in many natural systems, such as weather and climate (read “Chaos theory explains why weather & climate cannot be predicted beyond 3 weeks” ). This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in several disciplines, including meteorology, sociology, physics, computer science, engineering, economics, biology, and philosophy. A traffic model was developed showing that the system dynamics can pass under certain conditions to chaos.
Moreover, I consider that the movie Jurassic Park  gave quite a good and as accurate as possible explanation for chaos theory. Take a look and let me know what you think:
In the end, there are a couple of books I would like to recommend for this topic:
Main Source: Wikipedia;
There are many other sources for learning about chaos theory (especially because it has so many application in different other sciences) and I advice you to search and give it a try. At least a small glance over it and some of its wonderful concepts will make you see the world with different eyes.
Let me know your January favorites in the comment box bellow. Have a great day. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram and WeHeartIt. I will try to post there as often as possible.
Don’t forget that maths is everywhere! Enjoy! ~LThMath~