Intrinsically Defined Curves

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.