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.

Mandelbrot Mosaic

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.

Greyscale Mosaic---WARNING: the full sized image is about 95 MB

Nebulabrot Renderings

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.

Stellar DustTricorn


LotusAngle of Chaos


Cosine Conjugate

Newton Fractals

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.

A rendering of a Newton fractal.  See for details.A rendering of a Newton fractal.  See for details.

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.

LightningPurple Lightning

Harvest FestivalSpring Flowers

Controlled ChaosThe Eye

Yellow TwistCoffee and Cream

Burning SeasFireworks

Celestial ElephantsGecko Valley

StarburstIndependence Day

Sixfold in RedSnowflake

GangliaIsland Surf


Filigree in BlueSanddollar

Purple HexCircus Elephants

Blue PaisleyJulia in Purple

Pastel DragonCrimson Spiral

One Response to Gallery

  1. jason says:

    amazing pictures!!! true beauty!

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