Space-Filling Curves - Numberphile
Henry Segerman shows us some 3D-printed space-filling curves, including the Hilbert Curve and Dragon Curve. More links & stuff in full description below ↓↓↓ Check Henry's book about...
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So we're going to talk about space-filling curves. So... already that sounds sort of, counter-intuitive, like a curve, is like a one, like its a very skinny one-dimensional thing but space is like... ...two-dimensional or something so how can you have a curve? That fills up everything in space? So... We're going to build a curve starting with something very simple and then we're going to sort of change it. Uh, so, lets start with, this curve here. So this is three sides of square. So at the moment this is really not very, space-filling, right? Its just three lines, so we need to kind of make it more squiggly and we'll get there. So lets draw a grid, on this, so... Like, four squares, and so my curve is like going through the centers of those ...
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So we're going to talk about space-filling curves. So... already that sounds sort of, counter-intuitive, like a curve, is like a one, like its a very skinny one-dimensional thing but space is like... ...two-dimensional or something so how can you have a curve? That fills up everything in space? So... We're going to build a curve starting with something very simple and then we're going to sort of change it. Uh, so, lets start with, this curve here. So this is three sides of square. So at the moment this is really not very, space-filling, right? Its just three lines, so we need to kind of make it more squiggly and we'll get there. So lets draw a grid, on this, so... Like, four squares, and so my curve is like going through the centers of those ...
