Fiery Dragon (1990)

Martin Gardener tells the story of how this curve, first discovered by John E. Heighway, used by William G. Harter as a decoration symbolic of cryptic structure, and later analysed by them and another colleague, Bruce A. Banks. Though its final structure is complex, its description is not. The following two transformations are required to generate this shape:

xform
        scale { sqrt(2)/2 }
        rotate -45

xform
        scale { sqrt(2)/2 }
        rotate 135
        translate 1.0 0.0

Beginning with a single point, the whole curve can be generated by repeated application of these two transformations. This specification of the shape in terms of contractive, affine transformations is called an iterated function system (IFS).

This image of a dragon curve was created by covering with disks (spheres) the parts of the plane which do not include the fractal. These parts are determined by computing the minimum distance from a point P to the fractal. If this distance is d, then a disk of radius d can be drawn about the point P and all points inside that disk are known not to belong to the fractal. Click here to see a movie which illustrates this process at work.

Like many of my other works, I've used rayshade to ray-trace this image. This process creates the final image (which you see above) by simulating a camera inside the computer.