GeoGebra Art

In the classes I teach I often use GeoGebra for demonstrations; I assign GeoGebra constructions as homework, and our senior math majors use it in their oral presentations. GeoGebra, if you don’t know, is a Java-based dynamic geometry program freely available on the web. GeoGebraTube has thousands of applets developed by members for use in the classroom.

Now, GeoGebra is used mainly by high school teachers, and most of the applets available online are developed with that in mind. But the emphasis on algebra and coordinates by state curricula means that the program’s possibilities are vastly curtailed in common practice.

In trying to explore the software’s capabilities, I’ve set myself the task of constructing some of the fractals described in Mandelbrot’s Fractal Geometry of Nature. Images of my first attempts are shown below. At this point I’m not going to go into what makes a fractal a fractal, contenting myself merely with the following quatrain, which comes from Jonathan Swift:

So, Nat’ralists observe, a Flea,
Hath smaller Fleas that on him prey,
And these have smaller Fleas to bit ’em,
And so proceed ad infinitum.

Click on an image to view the slideshow and read the captions. Interactive versions can be found by going to my GeoGebra profile page. I won’t expand on my cleverness in the succinct programming that produced these images, but some of them are extremely clever.