Arjen Davidson

Abstract:

Fractals are used to predict or analyze various biological. Fractals are also helpful for geography. Fractal mathematics also known as complex geometrical shapes. Fractals, also known as repeating images. Fractals are connected by coordinates. Coordinates add more depth and detail onto the fractal as the number of Iterations continues to increase. The most common 2D fractals are the Julia and Mandelbrot set, my hypothesis is that if I make a Mandelbrot set and a Julia set as similar as possible without changing formulas then I will be able to discern their similarities and differences easier. The Mandelbrot set one the left with the Julia set to the right. I have made these Fractals black and white and left the past iterations visible, The Mandelbrot set seems to have a defined central body while the Julia set does not. Also the Julia set has a much less defined shape and is not symmetrical like the Mandelbrot Set. As you can see they both started with a circle as its first iteration; this was probably because they are both based on combining two complex numbers and evaluating them over time. This experiment is about fractals and the differences between the Mandelbrot and Julia set. The Mandelbrot set has a central body and is symmetrical while the Julia set is not. I might have been able to change a few more things without changing the sets and in the future I could do a similar experiment.

Awards Won: US Air Force Award