Fractals

CORE DEFINITION

Fractal (from Latin: frāctus, meaning 'broken' or 'fractured'), also known as fragmented or residual shape, is typically defined as 'a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,' i.e., it has the property of self-similarity. In mathematics, a fractal is an abstract object used to describe things existing in nature. Artificial fractals often exhibit similar shapes when magnified. Fractals are also referred to as extended symmetry or expanding symmetry. If the repetition of the shape is exactly the same after each magnification, it is called self-similarity. An example of self-similarity is the Menger sponge. Fractals can be approximately similar at different scales of magnification. Magnified images of the Mandelbrot set show this pattern. Fractals also imply that details of an image repeat themselves. Fractals are similar to but different from other geometric shapes. When zooming in on a shape, one can see the difference between fractals and other geometric figures. If you double the side length of a polygon, its area becomes four times larger. The new side length is twice the old one, while the area increases by a factor of four, i.e., 2^2.