This is a standard Mandelbrot algorithm. The default number of iterations is 75 times log base 100 of the magnification, and the program runs until either the requisite number of iterations have been reached or the sum of the squares of the axes is greater than 100. Every time you click on a point in the set, you zoom in 2 times towards that point.

If the user wishes to change the default iteration base (75), they can input it into the text field and press return. If they wish to remove the default iteration multiplier of log base 100 (magnification), they can click the radio box and the multiplier will be set to 1.

The colours are determined by how many iterations it took a failed point to reach 100. The darkest colour is at .1*the max number of iterations. Each additional colour is .1 times that (except that the lightest is at .95).

The Mandelbrot algorithm is:

xnew=xold*xold-yold*yold-xorig;

ynew=2*xold*yold-yorig;

Back to the Mandelbrot applet.