Monster Curves ✦

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.

This was mathematical heresy. How can a one-dimensional object cover a two-dimensional area without crossing itself (infinitely many times) or turning into a blob? You don't need a PhD to understand the construction. It's built on a simple "copy and replace" rule, much like a fractal. 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. As mathematician Hans Hahn once put it: "The

Let that sink in.

A line can, in fact, behave like a square. The distinction between one and two dimensions depends on how you define "distance" and "covering." You'll see a beautiful, orderly maze that slowly