Geometry,
printed from code.

From exponential growth to the logistic curve

A single population grows without bound, predators can only cage it into a boom-and-bust cycle, and the honest fix is a population that limits itself: the S-curve.

Van der Pol and the birth of a limit cycle

An oscillator with friction that changes its mind. Small swings get pumped up, big ones get bled down, and everything meets on a single closed loop the whole plane falls onto.

The pendulum, the cat's eye, and a little friction

The pendulum is the spring with the small-angle lie removed. Putting the full sine back in bends its phase space into the cat's-eye pattern, and friction drains it.

The spring equation and the shape of simple motion

Where the spring equation comes from, and why its phase space is a family of nested ellipses that damping turns into a spiral.

Drawing differential equations as wind

An old widget of mine, rebuilt in plain javascript, that draws the phase space of a differential equation the way those wind maps draw the wind.

Evil Cauliflower

Clearing some stuff out

New Feature - Download demo image

Symmetric - almost