This applet models a slightly different generating function than the Mandelbrot set. The Mandelbrot set is generated by zn+1=zn2+C, C being the point on the graph, with z0=0, whereas this figure is generated by zn+1=zn2+K, with z0 being the point on the graph, where K is some variable complex number. We write this number K (which we can vary, so as to make different pictures) as x + iy.
Click on in to zoom in to see greater detail, and out to zoom out. Likewise, click on right to move right, and left to move left. Click on Kx+ to increase the real part of the number K, and Kx- to decrease the real part, and click on Ky+ to increase the imaginary part of the number K, and Ky- to decrease the imaginary part.
The points calculated to be in the Julia set are colored black; the other colors code for the number of iterations before the point diverges. Note that a single color on the graph can code for several different values of divergence. The color scheme used in this applet was designed to give an "organic", "naturalistic" feel to the graph, by using the colors of earth, leaves, and sky.
© 2004-2011 by Lawrence T. Sein. All rights reserved.
Send questions to: lseinjr@hotmail.com