Home > Appreciation, Geometry > Hilbert Curves

Hilbert Curves

This is a cool sculpture inspired by a Hilbert curve, made from what looks to be left-over metal piping.


A Hilbert Curve is constructed through an iterative process that is repeatedly self-similar.  You start with a simple, bent path around the inside of a square, and then you take each straight part of that path and bend it to make it look what you started with.  And repeat.  Ad infinitum.

Given the infinite self-similarity (and some other properties), the Hilbert curve is a kind of fractal.  A nice visual illustration can be found at Wikipedia:  http://en.wikipedia.org/wiki/Hilbert_curve.

What’s especially interesting about Hilbert curves is that they essentially “fill up” the plane.  This is seemingly paradoxical, in that you have a one-dimensional object (a path) that ends up equivalent to a two-dimensional object (a plane).  For this reason, these are also referred to as space-filling curves.

I already have one plant that might be a fractal; I’ll be on the look-out for a space-filling vine!

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