Chaos

Chaos theory is an area in not just math, but physics, meteorology, and various physical systems. The underlying principle is this: a small change in initial conditions of any system results in a vast variance in the end results which can fluctuate a lot. It all starts in math. Take a variable x and subtract it from 1, then multiply it by x and a number r called the parameter which also varies. It is seen that for whatever input is fed into the equation, a fixed range of values is obtained called the attracting cycles of the system. However, when the value of the parameter exceeds 3.57, the outputs fluctuate over undefined patterns called bifurcations. This chaotic behavior is explained in a logistics map. In meteorology, or the study of weather, the so called 'butterfly effect' is a hypothetical phenomenon where a minuscule flap of a butterfly's wings would perhaps result in a drastic change in atmospheric conditions on some other part of the world which may express in the form of a storm. In psychology(shudder), a white lie can also translate into a social catastrophe. A problem, called the Fermi-Pasta-Ulam paradox stated that the expected behavior of physical systems was to be ergodic, but it is in fact, periodic. Ergodic means that the behavior is random. This periodic behavior was termed as FPU recurrence. This paradox was elegantly solved by a math professor and his students.