In here you will be able to experiment with the Classic Mandelbrot and Julia Sets of the map
K(z) = z*(d*z2-d+1);
with d a complex number.
What you will see is part of the complex plane. Each point corresponds to a value,either of d (Mandelbrot Set) or of z (Julia Set), and each color represents the number of iterations of function K(z) that it takes to leave a circle of a given radius around the origin.
This is a cubic function, unlike the Mandelbrot and the Logistic Function that are cuadratic. See the paper of Rogers and Whitley for a description of the dynamics of this function.
Scroll down to the end, then click the START button. The classic Mandelbrot Set for function K(z) will be generated. You can magnify the Mandelbrot Set as before, or explore the awesome Julia Sets.
After switching to Julia mode, you can select a point within the Mandelbrot Set by clicking on it. This will be the parameter c for generating the corresponding Julia Set. You can, now, explore this Julia Set by zooming into it as you did with the Mandelbrot Set. To select a new parameter value RESET the process.
|Mandelbrot & Julia:|
|Try the other beautiful mathematical experiences on this site. Experiment with them, and, who knows you may discover properties that no one ever thought about. And in the future, College students will learn about it...|