Welcome to the Infinite World of Fractals!

What are fractals? Where do we find them? How are they made? Why should we care about them? What are they good for? These are some of the questions we'll be looking at through this online fractal course.

Fractals are complex patterns that show the same details at different scales. This means you can zoom into a fractal and find the same pattern deeper and deeper.

Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots.

We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightning bolts, blood vessels, flowers, etc are all examples of natural fractals. We can look at a fractal as a picture that tells a story of the natural processes that formed it. One of the great things about fractals is that even if you don't think you know anything at all about fractals yet, you actually already do, because you've grown up in a world full of fractals.

A fern is an ancient, primitive plant that exhibits self-similarity. Photo courtesy of Jonathan Wolfe.

We will also discover fractals made by computer, using simple algebraic equations calculated over and over. These fractals are particularly fun because they go on forever - that is they are infinitely complex. Explore the edge of the Mandelbrot Fractal below by clicking on it.

Click mouse to Zoom In           <Ctrl>-Click mouse to Zoom Out           Add <Shift> to Zoom faster

Both natural and mathematical fractals can be extremely beautiful, and one of the extraordinary things about learning fractals is to discover that science, math and art are intimately related.

Fractals are full of meaning. They are patterns that tell stories. Fractals are the pictures of Chaos Theory, the study of unpredictable, dynamic systems. We will use fractals to learn the fundamental lesson of Chaos Theory, that small changes can lead to big differences

Finally, fractals can be very useful, and we will some examples of fractals in engineering, medicine, electronics, and even in the design of cities.

Studying fractals can lead to a deeper understanding of the patterns of nature and the ways in which a wide range of seemingly different systems are actually interconnected.