Honorable Mention: Mysterious Fractal Flow

This image is of a fractal phenomenon I've discovered called fractal flow. In this case, it's how the Julia set of a random complex function flows around its domain(the complex plane) as the parameter c changes. The result is the meromorphic function you see before you. It is the product of many zeros and poles. Like the random complex function's Julia set, this meromorphic function is a fractal as well. The colors indicate the coordinate velocities of different parts of the fractal. Red is positive real, lime is positive imaginary, cyan is negative real, and purple is negative imaginary. The whiteness is the intensity, so complex infinity looks white. I'm currently investigating the complex dynamics of iterative systems and their orbits. Fractals are fairly good systems for testing such things. For instance, points inside the Julia set never diverge to infinity, and stay constrained to the set's interior. There they travel along various orbits. I will be researching the dynamics of these orbits for Julia sets with several different orbits. Specifically whether points are capable of jumping between orbits, and how chaotic the dynamics are. Because these points never diverge to infinity, their fractal flow is complex infinity. The aforementioned random complex functions have what are known as critical points. Each critical point has an associated Mandelbrot set. Values of c close to the edge of a Mandelbrot set tend to be the most intricate. Fractal flows with multiple Mandelbrot sets oftentimes have a disconnected dust of smaller versions of themselves.

Images 3 and 4 were generated using the same random function. My code is designed to set the location of all critical points are so that all the Mandelbrot sets can be used to find interesting values of c. For whatever reason, this complex function had an extra Mandelbrot set which my code didn't prescribe. This fractal flow was made using a value of c close to this mysterious Mandelbrot set. I will have to investigate whatever led to its mysterious existence.