The pulleys and gears for this were made using the makerbot 3d printer.  Each link scales down by a factor of .87 as do the orange strips of vellum.  An arduino controls the servo which drives the smallest gear.  Because all of the links scale down relative to the link before it, and the links maintain a constant angle (more or less) between pairs, the spiral is logarithmic (more or less).  The crossed belts (made of sting and plastic pulleys) act like gears and maintain the angles between links.  Eventually I will make a similar sculpture using gears instead of pulleys and belts.  I might add sensors to this sculpture to make it respond to environmental changes.

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