Fractal Graph 3

by henryseg
  • White

    White nylon plastic with a matte finish and slight grainy feel.

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This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 3, and has the incident edges arranged either in a 'T' formation, or like a corner of a cube. The vertex is replaced at the next step by a subgraph of a 3 x 3 x 3 cubical grid, the choice determined by whether the edges meeting at the vertex are in the 'T' or 'corner' shape. Each edge is replaced at the next step by four parallel edges, joining to the midpoints of the sides of each 3 x 3 face of the 3 x 3 x 3 cubical grid. We begin the construction with the first step being three edges meeting in a corner formation, and this is the result at the fourth step.


IN: 4.193 w x 4.193 d x 4.193 h
CM: 10.65 w x 10.65 d x 10.65 h


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great recursive sculpture!
April 13, 2014, 1:23 pm
Good to know that the edges are too thin to be polished, and yes, Shapeways' customer service has always been great for me as well.
October 19, 2011, 11:27 pm
I just received this item in WS&F and it is very a beautiful piece. I originally ordered it in WS&F Polished but I was promptly notified by Shapeways staff that it had some defects and they even sent photos of it and offered it at a discount. I elected to have it redone and they did in WS&F and REALLY fast. The best customer service I have experienced is without equal. Thank you Henry Segerman.
October 19, 2011, 10:15 pm


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