The interactive illustrations presented here rely on a Web technology called "inline SVG": Scalable Vector Graphics included directly within an HTML document. A simple test suggests that your browser doesn't support inline SVG. If you think the test result is wrong, by all means try clicking through to the illustrations with the links below. If you have trouble, you might try a different browser. Browsers that should work include the latest versions of Internet Explorer (versions 9 and 10) and recent versions of Chrome, Safari, Firefox and Opera.
"Crinkly Curves," in the May-June 2013 issue of American Scientist, discusses a family of geometric curves that are so zigzaggy they burst the bonds of one-dimensionality. The simplest example is the Hilbert curve. Successive approximations to this curve are more and more crinkly, and in the infinite limit the curve is all right angles. Presented here are two interactive illustrations that explore the nature of the curve.