Photorealistic Fractals

Blue Underwater Mandelbulb Octopus Curls

Sections:
1. Mandelbulb 2. Icebox 3. Mandelbox 4. 3D Burning Ship 5. Snowflakes 6. Experiments!

Using the physics of light waves, the Mandelbulb and other 3D fractals can be rendered with the optics of a camera lens, as if you photographed them inside a virtual world. The Gaussian thin lens equation describes how light bends through a camera lens and focuses the image on the sensor.

An illustration of light passing through a convex thin lens. Three rays are emitted from a point 1/d_o away from the lens, pass through the lens, and are bent toward each other so they intersect again at a point on the other side 1/d_i away from the lens.
1d_o + 1f = 1d_i

where:
d_o is the distance to the object.
d_i is the distance to the image projected on the camera sensor.
f is the focal length of the lens.

I wrote a custom GPU-based program to render the images in tiles, with multiple passes for supersampling. It has a virtual camera with a lens and a focal length, which I've adjusted so that the most interesting parts are in focus. Without a depth of field, the details are often difficult to see against a background of infinitely many more self-similar details. The focus gives objects a sense of depth when the background is decoratively blurred and the focal point becomes highlighted. The camera lens's diameter also adds a reference scale to the image. Without it, the fractal would look identical at all scales!

Click any image to see it in higher quality, full screen.