Mandelbrot Set (plus bonus chaos game)
This page contains links to local versions of some applets created by David Eck at Hobart and William Smith College.
View the Mandlebrot set. The computations allow for almost infinite zoom-in. Really cool! Includes a lot of beautiful curated examples.
An animated gif taken from Wikipedia.
Other examples of fractals. Fun to play with. Plus more beautiful curated examples.
Description of the Mandelbrot set
The Mandelbrot set is actually the region that you see colored in black when
the applet first starts. (You can change the color using the "Mandelbrot Color"
menu.) More exactly, black points are possibly in the set, but for some
black points, more computation would show that they are not really in the set.
Colored points are definitely outside the Mandelbrot set. The color depends on
the number of "iterations" that are computed before it is determined that the
point is not in the set. Points that are closer to the set require a larger
number of iterations. The "MaxIterations" menu determines how many iterations
the program will compute for a given point before giving up and coloring that
point black. Increasing the maximum number of iterations might change some
points from black to colored. For example, look at Example number 4.
This example has some large black areas, but if you increase the number of
iterations in the "MaxIterations" menu, you will see that some of the black
area should actually be filled with color.
Java versions
The following Java versions of the Eck's Mandelbrot applets have a few more capabilities than the Javascript applet above. You can download them and they should run by double-clicking.
This is like the Mandelbrot viewer applet. It has some additional features. Two features that I like are:
1. You can easily save images.
2. Select 'show orbits' from the tools menu. This shows a nice burst of points representing an orbit when you click anywhere on the picture. Clicking near the edges of the set produces the most spectacular displays.
This shows the orbits in lots of colors. There is a slider that controls the number of points displayed for each orbit. Holding the control key while clicking displays the orbit as a polygon. All very pretty!
Maybe Java runs in your browser
Just in case your browser can run Java applets here are xMandelbrot and MandelbrotOrbits configured as applets.