Image credit: Axel Rouvin, Wikimedia; image source; larger image

Nonlinear Geoscience: Fractals

Look up at the clouds and look at the patterns you see. It turns out that if you zoom in or out, you still see the same patterns, a property mathematicians call self-similarity.

In Nonlinear Geoscience: Fractals, notice how the streambed in the photograph has divided again and again, showing the same structure at different scales. The streambed and the sky are only two examples of the many fractals found in nature.

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Fractals Unit: Iterative Formation

You don't have to graph complicated equations to create your own fractal--you can create your own on plain paper by following the directions at Fractals Unit: Iterative Formation. There are several simple patterns you can try, such as the Von Koch curve.

(This feature was updated on September 2, 2013.)

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image credit: Wolfgang Beyer (Wikimedia Commons); image source; larger image

Benoît Mandelbrot, Novel Mathematician, Dies at 85

This famous fractal is the Mandelbrot set. Click to make the image larger, and look at the boundary between the black and blue--it is made up of the larger image, at smaller and smaller scales. Check out this Fractal Geometry page from IBM, especially the video (scroll down) that zooms in on the Mandelbrot set.

The image is named for Benoît B. Mandelbrot, who made it by graphing a set of complex numbers described by an equation. He coined the term "fractal" and popularized fractal research by showing its importance to other fields besides mathematics. Read more about his life and accomplishments at Benoît Mandelbrot, Novel Mathematician, Dies at 85.

Sprott's Fractal Gallery

Fractals are an emerging form of art. Using mathematics, artists can create colorful and otherworldly visuals. To learn more, visit Wikipedia's Fractal Art, and check out "Fractal of the Day" at Sprott's Fractal Gallery.