IF YOU TAKE A CLOSER LOOK AT NATURE around us, we find that many natural phenomena are not so simple as are often found in textbook examples. For example, floating clouds in the sky, turbulent water flowing in mountain streams, dancing flames in fireplaces, all show very irregular, ever-changing, unpredictable motion that makes us gaze at them always with pleasure.
   We find, however, that underneath the unpredictability and irregularity of nature lurks a strange form of order that has been cast as universal forms of chaos in time and the fractals of space. The chaos is an irregular, unpredictable motion in nonlinear deterministic systems, which are best represented by the 'butterfly effect': the flapping of the butterflies wings in Peking may develop into a thunderstorm in New York. In complex systems, new principles such as this can be found due to distant equilibrium fluctuations, strong non linearity, positive feedback, and self-organization.
   An important lesson to be gained from the study of these complex systems is that the whole is more than a simple sum of its parts. The complex systems exhibit emergent patterns by self-organization, which can be applied to synchronous flashing of fireflies, firing of neurons in the brain, circadian rhythms,

market behaviors, and even social networks. In fact, the frontiers of complex system research encompass almost the entire area of science and beyond.
   In fact, a simple search of the internet with the key words 'chaos' 'fractals' and 'complex systems?lead to enormous number of hit in mathematics, physics, biology, statistics, chemistry, electronics, mechanical engineering, computer science, chemical engineering, and even philosophy, sociology, economy, geology, linguistics, music, and paintings. 
   According to the famous physicist Joseph Ford, chaos and the science of complexity represent a new trend in modern science in examining the world of complexity around us. The innovations in computer technology and the rapid growth of nonlinear science led to the explosion of research on the complexity of nature. The knowledge of chaos and fractals helps you to navigate this seemingly strange world around you.