Intrinsically Defined Curves

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This plots a curve whose local curvature varies according to the choice of curvature function and multiplier. A broken-line path starting at a given position can be defined by describing a specific series of turns. More generally, you can use a function that determines the curvature at each point along a curve. Such a curve is said to be intrinsically defined. In biological systems, curvature often occurs when material is added to one side faster than another. The curvature functions in this Demonstration can be thought of as simple choices for how this difference could vary over time. They yield a variety of ordered and disordered structures.

Contributed by: Kovas Boguta and Fred Meinberg (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

curvature function — the local curvature as a function of arc length scaling factor — multiplies the curvature function



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