I don't know the name of this thing, please contact me if you do. It is built from a description my dad gave me.
The inner shape, which may change, is projected around an enclosing circle by doing the following: Draw the tangent line for each point on the inner shape, this line intersects the enclosing circle at two locations. For each of these locations draw another tangent line, the point at which these two lines intersect is on the projected shape.
In my implementation, the inner shape may be dragged with the mouse, the enclosing circle's radius may also be adjusted. The shape is formed from a collection of points. As you move a point on the line the surrounding points move in the same direction with a magnitude determined by a Gaussian distribution. The derivative of a point on the shape is estimated with the secant line through its two adjacent points.
It's main limitation is that no new points are added to the shape as it is stretched. This leads to the line moving in unnatural ways as it is stretched or compressed too far.
You can play with it below. Start by slowly dragging the thick black circle. You can change the size of the blue circle by dragging it as well. Ignore the random stray lines and dots, just a few bugs I don't feel like fixing yet.