Fractal Materials

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Here are some fractal materials studying how higher ordered space can be derived from a lower order space, plus a constant representing the minimum material thickness.  These were laser cut from 2.7mm plywood.  Enjoy ^_^!.

Here is a Hilbert space filling curve.

Hilbet space and negative space.

Another Hilbert curve laid out on an isometric gird. Actually, it appears that Bill Gosper, first discovered this shape.  I'd encourage you to explore these on your own.  As far as I can tell, there is an infinite number of fractal patterns.  Some are more compact than others, only "dimensionally fundamental" symmetries are allowed.

Isometric Hilbert space filling ribbons.

 More Isometric Hilbert  Gosper curves with three fold symmetry.

Three fold isometric Hilbert curve.

 Squishy space is squishy.  This was cut from a quite ridged sheet of plywood.  Not to ridged anymore.  Normally wood can only bend in a single direction.  Not so for this shape.