Iteration Color Scheme

The Iteration color scheme is for outside points only, since inside points never escape they all have the same iteration value. The way this scheme works is that we take the escape iteration of the point's orbit, and divide by the maximum iteration being used. This gives a decimal number between 0 and 1, we then take the palette color at that decimal number. So if the maximum iteration is 100 and the point's orbit escaped on iteration 27, we calculate 27/100 = 0.27, and we take the color from the palette at position 0.27.

With no smoothing, this produces the "old school" banding outlines.


There is an outline feature that allows the user to set all of the final iterations to a single color. This creates an outline border to the fractal image and reduces the "static-like" affect close to the set. To change the outline color, double-click on the color box and select the color. The "use for last" box is the number of iterations at the end that should be given the outline color.


The program offers two smoothing modes that blur the iteration escape levels, bands, you get in the image. One is a polynomial smoothing algorithm that requires the use of the degree of smoothing. Although this is called a polynomial smoothing algorithm, it works well for anything that is polynomial-like, i.e. az^n + bz^k + ... + c where the exponents are real number constants. The degree of the smoothing algorithm should be the same as the degree (highest power) of the polynomial-like function. So for the Mandelbrot set the degree should be 2 and for z = z^1.5 + c it should be 1.5.


The other smoothing algorithm is an exponential smoothing algorithm that works well for more general iterative systems as well as the polynomial-like systems. Exponential smoothing does not require a degree and can use straight or normalized modes. Normalized mode tends to give a softer glow to the edge of the fractal with the color palette styles in this program.


Below are images of the Julia set for (1 + 0.2i)sin(z) without exponential smoothing and with exponential smoothing.

Without


With