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| Hilbert designed a curve that wiggles so much it fills up the unit square. The first six steps in the construction are seen here. (One of the simplest ways to write the instructions for building these steps is by L-Systems.) | ||||||
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| So a curve, which we think of as 1-dimensional, can be so convoluted it fills up a square, which is 2-dimensional. | ||||||
| Remarkably, constructions very much like this occur in nature. |
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