I would like to create procedural paisleys. For my purposes a paisley is a curled teardrop shape (google image search) composed of multiple shells. I think it best to exclude the ones that have spiral tails.
My first attempt was to use (piecewise) a semicircle for the head and two simple spirals for the sides of the tail. I consider my first attempt a failure, because the junction between the tail and the head has a sharp angle (I guess you could say that the derivative of the function was discontinuous on the theta coordinate when expressed in radial coordinates).
What are some better formulas to generate the shells of a an object that would be recognized as paisley-shaped?
(p.s. feel free to give this question relevant tags, I'm just guessing)
For now I have kludged a fix using cubic Bezier curves. Since the control points of the Bezier make it relatively easy to control the tangent, they are a convenient way to bridge from the spiral to the semicircle.
The next task is to align graphical elements at different insets, but that is a rabbit hole for another question which I may return to another day.