Our 3D-fractal sculptures
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A brief mathematical overview
The 3D Hilbert fractal is a type of space-filling curve, a curve that passes through every point in space. A "discrete" Hilbert curve in 3D goes through finitely many lattice points; our filament sculptures pass through 26 = 64 points, or through 29 = 512 points for the laser-scribed model (the infinite-order true Hilbert curve would of course go through an infinite number of points). Our filament designs have the beautiful properties that a) each short run of the Hilbert fractal is straight, b) each run goes in an ortho-direction (x, y, or z direction exclusively), and c) the fractal starts and ends at the sculpture's base, allowing for elegant mounting.