The study of science has always tried to model the present phenomena to predict the future. With different fields of the study of science evolving with the same goal, a modern branch of study has developed which finds its basics in the famous quote “The present determines the future, but the approximate present does not approximately determine the future”. Chaos Theory has recently turned fifty, celebrating more than half a century of flapping butterfly wings in Brazil and creating tornadoes in Texas. It was a meteorologist named Edward Lorenz who first outlined why seemingly consistent and knowable systems can still go wildly wrong. Fractals are geometric shapes that are very complex and infinitely detailed. You can zoom in on a section and it will have just as much detail as the whole fractal. They are recursively defined and small sections of them are similar to large ones. One way to think of fractals for a function f(x) is to consider x, f(x), f(f(x)), f(f(f(x))), f(f(f(f(x)))), etc. Fractals are related to chaos because they are complex systems that have definite properties.
The word fractal was first introduced by Mandelbrot and Ness (1968)and laid the foundations for fractal geometry. He also advanced fractals by showing that fractals cannot be treated as whole-number dimensions; they must instead have fractional dimensions. Calculation of fractal dimensions or rather measuring self-similarity has been a major area in the field of study of chaos.

If we ask “How long is the coast of Britain,” the answer is that it depends on how closely you look at it, or how long your measuring stick is. A more realistic answer is: the coastline gets longer and longer as you measure it more closely, and it approaches infinity. In fact we can never tell how long the coast is, but can rather talk about its fractal dimension, making it a very useful concept to describe a coastline. Like the coast of Britain all natural events have their nature of self-similarity embedded within them as for example the sound waves coming out of our mouths as we speak, or the ECG time series from our hearts when we get diseased, or the EEG time series from our brains when we think and even the ups and downs of share prices. With this idea, the analysis of the fractal structure can be used to predict the emotions of speech, diagnose the diseases and even predict share prices.