Mandelbrot Mysteries

These are artistic variations of the Mandelbrot set, from years of experimenting with the equation, inventing new ways of drawing it, and tinkering with the mathematics. Whenever something interesting happens, I save the image. Just like paintings and other works of art, they're the result of inspiration, creativity, and a smidgen of luck. And some of these unique works will never be duplicated, since the equations are lost in the depths of my code history and incompatible with my current interface, or gone entirely due to my GPU driver crashing before I saved it.

I've grouped the art by the period's style it reminds me of:

The Classical Period

These are grayscale drawings of what seems to be an "inverted" Mandelbrot set. I was experimenting with the equation to create more detail inside the fractal set, and accidentally blew it up to make a giant copy of the Mandelbrot set outside the primary one. It was a ghostly dust of points, with no substance or pattern. I experimented with constant factors for the new equation, and found that with a value of precisely 0.01 an incredible amount of detail emerged from the noise. However, anything beyond ± 0.02, and everything will vanish! Even with the magic value of 0.01, there is still a considerable amount of noise. On the last two images, I applied supersampling to reduce the noise, but it lacks some of the artistic charm. They remind me of sketches and music from the Classical period.

The Romantic Period

These images are results of my experiments to create colorful details outside the Mandelbrot set. In the equation, each iteration refines the fractal boundary, and since it's a smooth function, the new boundary must have a smooth curve. Those are the bubble-shaped curves in the images, approaching the true boundary of the fractal with each iteration. The sweeping colors remind me of Post-Impressionist paintings at the end of the Romantic era.

This one reminds me of Van Gogh's 1889 painting, The Starry Night.

The Baroque Period