algorithm

1138: The Power of Many

| wonko

I love the geometric world of Tessellations, and have folded many. It is doubly satisfying when you design that tessellation molecule and how it tiles yourself.

This is a hex-point tessellation, and is based on a mathematical algorithm discovered by Aurélien Vermont ( @auregamiiii ) and described in a paper written by them as part of their study in Engineering. The algorithm describes a geometric construction method that lest you raise a n-finned spike from a flat surface and have the surface “heal” around it.

It does so by placing strategic dart pleats that seamlessly absorb the excess paper caused by the spike in a controlled and very flexible way. You can raise a spike at the intersection of a collection of creases (2 or more intersections). The folding gets progressively more fiddly the smaller the spike and the larger the number of intersecting lines.

I chose to derive a hex-spike, that is a 6-crease intersection spike molecule, based on a regular hexagon. Once I had derived all the creases necessary to allow one spike to be raised, I test folded it (just to check – theory and practice are sometimes at odds – some paper designs for origami seem to ignore the thickness of the paper which then breaks the symmetry or distorts the shape) and all was good.

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1124: Vase Algorithm

| wonko

I recently opted in to a “fold along” workshop (at 1am-3am local time) with Gerardo at neorigami.com and a number of guest demonstrators. The first model was a square “Vase” designed by Saburo Kase:

The process, starting with a “preliminary base” got me thinking about generalization of the algorithm to other regular polygons. The corner treatment is radially symmetrical (ie. you do the same thing on each corner), and has 3 “about here” judgement folds that all combine to control the final shape of the vessel …. so….

I cut an equilateral triangle, a new square and a regular hexagon, then formed “preliminary bases” from each geometry.

Next, I followed the corner algorithm on each of the 3, 4 and 6 corners respectively to see how it behaved. I now regret not also using a regular pentagon, as I think it would possibly be a “sweet spot” for the organic shaping … maybe some other time.

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