Monster Curves Updated · Fresh & Recent

But what if I told you that mathematicians have discovered curves that are so wild, so twisted, and so impossibly long that they can literally fill up a entire square? Not a thick marker blob. A true, one-dimensional line that visits every single point inside a two-dimensional area.

As mathematician Hans Hahn once put it: "The concept of a curve is far richer and more terrifying than anyone had imagined." You don't need infinite iterations to see the beauty. Open a simple Python environment (or even a spreadsheet) and generate the first 4 iterations of the Hilbert curve. Plot the points. You'll see a beautiful, orderly maze that slowly begins to eat the empty space. monster curves

If I asked you to draw a curve—a simple line from Point A to Point B—you’d probably draw a smooth arc or a wavy line. You’d leave plenty of empty space on the page. But what if I told you that mathematicians