Fractal charm: Space filling curves
A montage of space filling curves, meant as a supplement to the Hilbert curve video.
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If you watched my video about Hilbert's space-filling curve... ...you might be curious to see what a few other space-filling curves look like. For each one, see if you can figure out what the pattern of construction is. This one is the Peano curve. It is the original space-filling curve. But of course, there's no reason we should limit ourselves to filling in squares. Here's a simple triangle-filling curve I defined in a style reflective of a Hilbert curve. This one has the most delightful name, thanks to mathmetician/programmer Bill Gosper: "Flow Snake" What makes this one particularly interesting is that the boundary itself is a fractal. It might become a surprise how some well-known fractals can be described with curves. This is another famous fractal. The "Koch Snowflake" Let's finish things off by seeing how to turn ...
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If you watched my video about Hilbert's space-filling curve... ...you might be curious to see what a few other space-filling curves look like. For each one, see if you can figure out what the pattern of construction is. This one is the Peano curve. It is the original space-filling curve. But of course, there's no reason we should limit ourselves to filling in squares. Here's a simple triangle-filling curve I defined in a style reflective of a Hilbert curve. This one has the most delightful name, thanks to mathmetician/programmer Bill Gosper: "Flow Snake" What makes this one particularly interesting is that the boundary itself is a fractal. It might become a surprise how some well-known fractals can be described with curves. This is another famous fractal. The "Koch Snowflake" Let's finish things off by seeing how to turn ...
