Fractals are possibly the most fascinating discovery in the field of geometry in our lifetime. Fractal geometry is being used to model some of the most complex dynamic systems in all of life. They are being integrated in fields such as communication, computer animation, engineering, economics, and even medicine. Unlike Euclidean geometry in which everything is reduced to nice regular shapes, fractal geometry is able to describe the intricate patterns in nature that have baffled even the greatest mathematicians throughout history. Fractal geometry was first discovered in 1970 by the French mathematician Benoit Mandelbrot. Unfortunately at that time the math community was not open to such an innovative leap in geometry, and Mandelbrot was an outcast among his colleagues. Mandelbrot looked down upon Euclidean geometry because it was only useful for studying the world that we as humans created based on a number of pre-existent constants that enabled us to make sense of a seemingly chaotic world. Mandelbrot was quoted in his book
The Fractal Geometry of Nature (1983), as saying, "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." Once again the limitations of mathematics prevented humans from seeing a much deeper form of order that exist all around us. The math behind fractal geometry is surprisingly simple. It uses a basic algorithm that feeds a number through it and then loops the new number over and over again. This process, known as iteration, is very tedious and sometimes impossible to compute by hand. Fortunately, Mandelbrot was offered a job at IBM that gave him access to supercomputers that could do the iterations for him. This opened Pandora’s Box of possibilities in terms of what we could do with fractals. Mandelbrot plotted these millions of points and arrived at the famous Mandelbrot Set which can be visualized by applying a continuous color scheme to convey the necessary details that are fundamental to fractal geometry.
It didn’t take long for people to see that fractals were much more than a means of creating cool images. Next blog I will talk about the properties of fractals, their first implications, and how they are spreading like wild fire across all fields of science.
