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Hilbert cube variation (4th order, 1.5 mm)

Design by srjskam

(1)

4 out of 5
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(4) Comments

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Inside out...

In real life.

Inside out...

Resting on its back.

Size comparison. This is the leftmost.

A ridiculously detailed 4th order Hilbert curve* in 3D. Two corners are rotated so that the curve forms a loop.Thickness and gaps 1.5 mm.

See http://www.shapeways.com/model/109525/small_hilbert_cube_variation.html for a 1 mm version and http://www.shapeways.com/model/111039/tiny_hilbert_cube_variation__1_5mm.html for a 3th order 1.5 mm version.

* Actually Hilbert cube seems to have a different meaning.

cm: 4.652 w x 4.652 d x 4.652 h

in: 1.831 w x 1.831 d x 1.831 h

Comments

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srjskam says:

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@ttoinou Yes, the rules have been broken only at the highest level, ie 2 of the 1/8 blocks have been rotated along their space diagonals to make their ends meet. For example henryseg's curve uses a different way to make it cyclic, which might make it look more regular (especially at lower degree).

February 12, 2013, 1:35 pm

ttoinou says:

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Great! I'm planning to do one myself. Did you change the hilbert iteration curve ? Or the only modification you made is to rotate the two corners so that it loops ? I'm asking because there seems to be randomness in your fractal (I can see that from the picture).

February 11, 2013, 7:15 pm

srjskam says:

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A hollow Hilbert cube wouldn't be a Hilbert cube >_>... But it shouldn't matter much on the outside if 1/8 was removed from inside (not much savings there). Removing 296/512 (only leaving the first order 'wiggling' as a shell) would probably make it boring and hard to design without 'lifting the pen', and exceedingly wobbly (maybe it is already, waiting for the print...) Of course one could just leave the limitations of space-filling curves and adopt just the visual theme.

April 19, 2010, 11:16 am