Chaos theory may be a branch of arithmetic that specialize in the study of chaos—states of self-propelled systems whose apparently-random states of disorder and irregularities ar typically ruled by settled laws that ar sensitive to initial conditions. Chaos theory is associate degree knowledge domain theory stating that, among the apparent randomness of chaotic advanced systems, there ar underlying patterns, connection, constant feedback loops, repetition, self-similarity, fractals, and organisation. The outcome, associate degree underlying principle of chaos, describes however alittle modification in one state of a settled scheme may end up in massive variations in an exceedingly later state (meaning that there's sensitive dependence on initial conditions). A figure for this behavior is that a butterfly flutter its wings in China will cause a cyclone in American state . Small variations in initial conditions, like those because of errors in measurements or because of misreckoning errors in numerical computation, will yield wide branching outcomes for such self-propelled systems, rendering long prediction of their behavior not possible generally. this will happen despite the fact that these systems ar settled, that means that their future behavior follows a novel evolution and is totally determined by their initial conditions, with no random parts concerned. In alternative words, the settled nature of those systems doesn't build them sure. This behavior is thought as settled chaos, or just chaos. the idea was summarized by Edward Lorenz as Chaotic behavior exists in several natural systems, as well as fluid flow, heartbeat irregularities, weather and climate. It additionally happens impromptu in some systems with artificial parts, like the exchange and road traffic.