Friday, February 10, 2012

Sierpinski Pyramid

(From the right - Stage 0, Stage 1, Stage 2 and Stage 3)

After making the Sierpinski Triangle on graph paper, the idea of making a 3D version out of construction paper started preying on me. After a day or so, I decided to make a small one just to get it out of my system, by approaching it as a collection of "stage 0" triangles glued together. Stage 1 is just 4 stage 0's held together with wood glue. That worked out fast, so I figured that going to stage 2 would be easy enough. It just meant cutting out 16 equilateral triangle strips (for triangles 2cm to a side), folding and taping them up, then gluing them together. One sheet of construction paper yields 14 strips 1.8cm wide, with 8 substrips of 4 triangles each, plus one 3-triangle substrip left over. Initially, I cut all the individual triangles apart and taped them back together again, until I realized that that step wasn't necessary and I could just use the substrips as a whole. It took roughly 8 hours of cutting and taping (plus the gluing, not including the time for the glue to dry) to get my first stage 3. That used up just a little over half the sheet of paper, for 64 stage 0s. A stage 3 is roughly 16 cm wide, and 13 cm tall (6" x 5"). It's fine as it is, but the Sierpinski effect of having the central section removed repeatedly is just starting to become noticeable. In other words, I couldn't stop until I reached stage 4.

(Stage 4)

Stage 4. 256 stage 0 pyramids. 2.2 large sheets of construction paper. Over 30 hours of work, spread over 2 weeks. It's crooked because my only tools were a straight edge, scissors and a toothpick. But, because of its shape, it is structurally strong, and, with the glue added, it's still just a little over the weight of 2 pieces of thick paper (maybe a couple of grams). I'll stop here. Now, I just need to find a home for it...

(Stage 4 directly from the front.)

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