In here you will be able to experiment with the Classic Mandelbrot Set of the map
G(z) = b*z*(1-z);
with b a complex number.
What you will see is part of the complex plane. Each point corresponds to a fixed value of b, and each color represents the number of iterations of function G(z) that it takes to leave a circle of a given radius around the origin.
This function is called the Logistic or Verhulst Function. See the paper of Robert May 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 G(z) will be generated. To get "into" the set, click on any point of it and a magnification of order two will be generated. Keep on clicking to travel into the Set and go where no one has gone before... To start over click on RESET.
|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...|