Why Can Fractals Generate Algorithmic Art?

Fractals are structures defined by their self-similarity- they display repeating patterns at various scales. No matter how much we zoom in on a fractal, we keep encountering the same shapes, though they may be rotated or scaled differently. This property is used in generating algorithmic art as they can be created through recursive mathematical processes.

Behind the beauty of fractals lies recursion, a concept in which a function calls itself repeatedly to generate a sequence of results. The most famous example is the Mandelbrot set, defined by the equation:

Quadratic functions of the form f(z) = z2 + c, where c can be any complex number.

The function repeatedly applies the formula to generate a series of points. When plotted, these points form the fractal pattern we associate with the set.

Please read this interesting article to know more about the history of Mandelbrot Sets and the Math behind it.

https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/#:~:text=The%20Mandelbrot%20set%20deals%20with,can%20be%20any%20complex%20number.