A fractal is a geometric shape that has symmetry of scale. This means that it is a shape that you could zoom in on a part of it an infinite number of times and it would still look the same. This is also called self-similarity. Computer-generated fractals are produced mathematically, and these can create detailed pictures of mountains, plants, waves, and planets. Some mathematicians, such as Benoit Mandelbrot, study nature first, looking for fractal behavior.

Here are some sights to explore fractal landscape galleries. musgrave/landscapes.html

What's coming ...

Mathematically generated fractals can be made from both real and complex numbers. We will explore some of each.

One simple real number fractal is the Serpinski Triangle.

Fractals formed from real numbers are pretty, but you should see what complex numbers can do, like the fractal on this page. WOW! But, we must review our complex numbers first.

Now that you have refreshed your memory, let's look at what complex numbers can really do. Complex Fractals

Want to go back ?