Fractal Geometry

Fractal Geometry In the past, mathematics focused on collections and functions that can apply the classical calculus method. Collections or functions that are neither smooth nor regular are often called "pathologic" and are not worth studying. They are seen as personal curiosity and are rarely thought of as a class to which general theory may apply. However, this attitude has changed in recent years. Irregular collections provide a better representation of natural phenomena than classical geometry.

The latest development of geometry is fractal geometry. Fractal geometry was developed and promoted by Benoit Mandelbrot in his book "Natural Fractal Geometry" published in 1982. Fractal is a self-similar form (invariant to changes in scale) and is a geometric shape with fractional dimensions. As with chaos theory, that is, research on nonlinear systems, fractals are very sensitive to initial conditions and small changes in the initial condition of the system can make the output of the system significantly different.

An interesting element of chaos theory is a complex image called fractal. There is a close relationship between chaos and fractal. For example, fractal geometry is the geometry that represents the chaos system we find in nature. Fractal is a way to describe language and shape. Fractal geometry is described in an algorithm which is a series of instructions on how to create a fractal. The computer converts the instructions into patterns we see and calls fractal images. These same chaotic features also apply to mathematics. In order to create an image called a fractal, several equations can be repeated multiple times. Suppose that the two equations contain only one X and Y variable and some constants. When the equation is repeated multiple times, the result is drawn on the computer screen. Immediately, a very complex image (called a fractal) is magnified and the pattern repeats. Fractal shows all chaotic features