Nature is too chaotic for the traditional methods and equations used in these forms of mathematics. Something different was needed to explain, describe, and show the erratic shapes of nature. Enter, Benoit Mandelbrot. Mandelbrot, a mathematician born in Poland, has greatly advanced the study of nature, with his study of fractals. Since his initial studies of fractals, many scientists and mathematicians have started studying fractals.
Fractal geometry is the study of fractals.
Because of the possibility of using fractals to describe some objects in nature such as trees, coastlines, and mountain ranges, the study of fractals has become an increasingly interesting topic to mathematicians and scientists. Chaos isn't usually associated with mathematics. Usually when you think of math, you think of long equations, that will give you an exact, or close approximation, of the answer you are looking for. No chaos there, just direct questions, direct answers, and if you involve graphs, they are explainable, predictable graphs that describe the function. When we move away from physics and calculus, to nature, we turn to chaotic scenes.