Bedouin Fractal

Created by Paul Bourke
Attributed to Russell Walsmith
April 2016

See also: Visualising volumetric fractals

This is created by considering each point within some region of 3D space (x0,y0,z0) and evaluating the following series. The point (voxel in computer graphics language) is then assigned a scalar quantity depending on how quickly the series tends to infinity.

xn+1 = a + sin(x0)
yn+1 = b + sin(y0)
zn+1 = c + sin(z0)


a = xn2 - yn2 - zn2
b = 2 xn zn
c = 2 xn yn

Rendering here done using custom code to create the volumes and then the Drishti volume rendering software for the final graphics. The rendering technique is traditional volume rendering which includes assignment of both colour and opacity dependent on the voxel scalar quantity and also the estimate of local gradient to create a surface for the a lighting model.

The range for which the interesting part of the model exists is -1.5 to 1.5 on all three axes. The first three renders here sample that volume 1024 times on each axis between the bounds above, so approximately 340 samples per unit distance.

The next 2 images are a further 3 times zoom factor, namely 1000 sample per unit distance.