“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”
-Benoit Mandelbrot
Geometry was developed a long long time ago. And thanks to the computer a new kind of geometry became possible whose founder is Benoit Mandelbrot. That is known as fractal geometry. Fractal geometry which is known as nature’s geometry is not merely a branch of mathematics. Above that fractals help us to view the universe in a different manner. Extending beyond the typical perception of mathematics as a body of complicated boring formula, fractal geometry mixes art with science and mathematics to demonstrate that equations are more than just a collection of numbers.
To understand it in a better way, go outside of your room and look at the nearest tree. You can see a mathematical set that exhibits a repeating pattern displayed at every scale.
It’s not only present in a tree’s structure but also it is all around your life. It is in the waves of the ocean. It is in the nerves of the leaves, in the palm of your own hand, in your brain, inside your lungs, in the whole human body. It is the pattern found in this universe.
By definition, a fractal is a geometric figure often characterized as being self-similar.
Now, what does self-similar mean? If you look carefully at a fern leaf, you will notice that every little leaf-part of the bigger one has the same shape as the whole fern leaf. You can say that the fern leaf is self-similar. The same is with fractals; you can magnify them many times and after every step, you will see the same shape, which is characteristic of that particular fractal image.
Another important characteristic is the non-integer dimension. It is hard to imagine as the name suggests. Its is between integer dimensions eg: A straight line 1 dimensional whereas a fractal curve is between 1 dimensional and 2 dimensional. Famous fractals are Sierpinski Gasket, Von Koch snowflake, Mandelbrot set, Menger sponge, Julia set and Mandel bulb.
Fractals are useful when creating realistic landscapes and planetary surfaces in the film industry.
Fractal geometry is currently applied in many fields, eg; research in climate change, the trajectory of dangerous meteorites, helping with cancer research, by helping to identify the growth of mutated cells,
in astrophysics, DNA research etc.
Fractal art is largely prevalent in ancient Indian architectures and many south-east Asian temples and monuments exhibit fractal structure. The famous Eiffel Tower resembles a 3D structure of the Sierpinski triangle.
Fractal geometry in ancient Indian architecture
Many scientists have found that fractals are a powerful tool for uncovering secrets from a wide variety of systems and solving important problems in applied science. The list of known physical fractals is long and growing rapidly.
Author
