Magnetic Curves: Curvature-Controlled Aesthetic Curves Using Magnetic Fields

We describe “magnetic curves”, a particle-tracing method that creates curves with constantly changing curvature. It is well known that charged particles in a constant magnetic field trace out circular or helical trajectories. Motivated by John Ruskin’s advice to use variation in curvature to achieve aesthetic curves, we propose to continuously change the charge on a simulated particle so that it can trace out a complex curve with continuously varying curvature. We show some examples of abstract figures created by this method and also show how some stylized representational forms, including fire, hair, and trees, can be drawn with magnetic curves.