Automatic Generation of General Quadratic Map Basins

Julien C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA


Clifford A. Pickover
IBM Watson Research Center, Yorktown Heights, New York 10598, USA


In this informal article, we describe simple approaches whereby a computer can automatically select parameters and generate a large collection of diverse, aesthetically appealing fractal patterns based on general quadratic map basins. Computational recipes are included to encourage reader involvement. In essence, we describe methods for teaching a computer to be both an artist and a critic of its own art.

Ref: J. C. Sprott and C. A. Pickover, Comput. & Graphics 19, 309-313 (1995)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.

The computer source code escape.bas from the article is available along with an executable version escape.exe. You may also wish to view some images based on this technique and generated by the program Fractal eXtreme by Cygnus Software.