Just recently my friend told me about the interesting features of a fractal as he paid tribute to its popularizer, Benoit Mandelbrot, who was a product of Caltech. When I looked at a broccoli, which he cited as an example, I was really amazed at its weird shape. "Is this what they call a fractal?", I shrugged. Later, the striking images of colorful fractal patterns presented the astounding discovery to me. I felt as if a new window on the mysteries of Nature opening!
In 1975, Mandelbrot coined the term,"Fractal", which he derived from the original Latin "Fractus", meaning "fractured". He advocated that most of the things found in Nature are fractals, and continued to explain that "[c]louds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." ( The Fractal Geometry of Nature, 1982)
Fractals are rough, irregular or fragmented geometric shapes, which can't be described in merely Euclidean terms.
The pattern multiplies, whether it zooms in or zooms out, and the formation is continued by iteration. The formula which generated a Mandelbrot Set was a simple one. The individual parts displayed an amazing self-similarity, which makes the whole set a unique object of mathematical curiosity.
Fractal dimension is another key feature that draws our attention. It exceeds normal topological dimension. For example, the coastline of South Africa is 1.02 whereas the west coast of Great Britain is 1.25. A Sierpinski triangle has a space with fractal dimension of approximately 1.585. Thes proof establish the existence of a non-integer, fractal dimension, which was not known before.
Fractals are employed as models in research in varied fields. Whether it's plant growth or cloud formation, it mirrors fractal similarity. You can also use fractal structures to conform to the growth of marine organisms such as sponges and corals. Then, it goes to the extend of being used in the modelling of brain activity. Even in the stock market, it's now being utilized to observe the movement. So the study of fractals have infinite scope, no doubt.
