The usual Mandlebrot Set, colours points according to how many iterations of the formulae:

The java code corresponding to this formulae is:

I was interested in exploring points that don't head off to infinity. So I modified a Java program that I had written several years ago to explore the Mandlebrot set, in 2009 I used it to produce this icon. I allowed a maximum of one million iterations per point.

Z' = Z^2 - Zare required, before |Z'| is greater than 2. (Where the x and y coordinates of each point are treated as the Real and Imaginary parts of a complex number - after applying an affine transformation to relocate the origin and to scale the dimensions appropriately.)

The java code corresponding to this formulae is:

final double xb = x0 + xa * xa - ya * ya; final double yb = y0 + 2 * xa * ya; xa = xb; ya = yb;(x0 & y0 are the scaled values of the original point on the screen)

I was interested in exploring points that don't head off to infinity. So I modified a Java program that I had written several years ago to explore the Mandlebrot set, in 2009 I used it to produce this icon. I allowed a maximum of one million iterations per point.

(Note that although Java -- as of JDK1.6.0_16 -- produces a PNG formatted image, I had to use the GIMP to modify it so that Firefox could display it!)