A selection of images that have appeared on this website is below. Each section or image is linked to the entry in which it first appeared. This gallery is likely to be a continual work in progress, and will be updated periodically.
The Mandelbrot set can be seen as a map of the Julia sets. Specifically, if a complex number is in the Mandelbrot set, then the Julia set associated to that number is connected. An interesting application of this fact is discussed in this post. Both of the images below were constructed in this manner, though they have been scaled down for display here. To get the full effect, please download the linked images, though be warned that they are quite large.
These images were produced using the nebulabrot rendering technique. This technique gives one a way to visualize the dynamics of a Mandelbrot-style system rather than a static attractor.
During the last year of my master’s program at UNR, I took a two semester sequence on numerical analysis from my advisor, Dr. Eric Olson. One of the topics that we discussed was numerical root finding. This naturally led to some investigation of a rather interesting set of fractals, called Newton fractals.
Mandelbrot and Julia Sets
The following images are renders of various Mandelbrot and Julia sets. The mathematics behind these is described in greater detail in the Mandelbrot set series.