Quaternion Julia Set VRML Server

First, you will need a VRML plug-in for your browser in order to see the results. If you're browser needs one, I've found that the Cortona VRML viewer plug-in from Parallel Graphics works really well (instantly, no reboot needed).

Second, fill in the constants for the quaternion Julia set below. Re(c) and Im(c) denote the real and imaginary values of the constant c. Click any point on the Mandelbrot set to fill the Re(c) and Im(c) values in the form automatically. The parameter c should be a point inside the Mandelbrot set.

Theta is an angle that the complex Julia set is rotated before determining its quaternion extensions. Precision sets the resolution of the grid that the quaternion Julia set is computed on. The smallest allowed precision is 0.05, which can generate a megabyte of data in some cases.

Re(c):
Im(c):
Theta: Radians
Precision:

Reset Form

After you press the "Generate VRML" button you should see a 3-D quaternion Julia set that you can manipulate. The program can malfunction for a variety of reasons. If it consistently does not work, please let me know.

About quaternion Julia sets ...

For more information on quaternion Julia sets, see the following papers (all in Adobe's PDF format):

John C. Hart and Louis H. Kauffman and Daniel J. Sandin. Interactive visualization of quaternion Julia sets. Proc. of IEEE Visualization '90, Oct. 1990, pp. 209-218.
John C. Hart and Daniel J. Sandin and Louis H. Kauffman. Ray tracing deterministic 3-D fractals. Computer Graphics 23(3), Aug. 1989, pp. 289-296.
Alan Norton. Julia sets in the quaternions. Computers and Graphics 13(2), 1989, pp. 267-278.
Alan Norton. Generation and rendering of geometric fractals in 3-D. Computer Graphics 16(3), July 1982, pp. 61-67.

About the code ...

The CGI engine used to generate VRML quaternion Julia sets (source: vrmlqjs.c and q.c) was adapted from Jules Bloomenthal's implicit surface polygonizer.

Jules Bloomenthal. An implicit surface polygonizer. Graphics Gems IV (Paul Heckbert, Ed.), Academic Press Professional, New York, 1994, pp. 324-349.

The code was refined during a visit with Greg Turk in May, 1996. We used it to reproduce a parameter space visualization of a Mandelbrot set for quaternion Julia sets that Alan Norton discovered. Our results ended up as a figure in Jules Bloomenthal's Implicit Surfaces book.