Natural Patterns: Animations

Torus

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A punctured torus in motion illustrates Tai Chi's ability to melt away from incoming energy.

A stereographic projection of a Clifford Torus in four dimensions performing a simple rotation through the x-z plane.

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Spiral

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An Archimedes' Screw can use circular motion to propel an object along the axis of rotation, either forward or backward.

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A scroll compressor is used to compress gases.

Curve

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Three forms of Watt's Curve

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Watt's Linkage shows how linear force can be generated and dissipated by an S-curve.

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The Trammel of Archimedes, also called the Kentucky Do-Nothing, perfectly illustrates how two linked linear forces can produce not only an ellipsis but can be used to fling an object to some distance or pull it inward.