What to see
A wheel, consisting of coloured discs, rotating within a larger wheel, no doubt.
The story becomes interesting when you concentrate on and follow one single disc, e.g. the blue one – it moves in a totally straight line, horizontal in case of the blue disc. All single discs move in straight lines, but our visual system combines their composite motion into the gestalt of a wheel – although they differ in colour. The wheel motion is physically quite realistic, in fact inside a epicyclic gearbox it happens all the time, or more specifically in a “Tusi-couple”.
What to do
Click on the button entitled “Linear”. The wheel is gone, now there is some “see-sawish” motion, although all single discs still run on the same path! What has changed is the relative phase, that is “where is the green disc when the blue disc is leftmost?". The slider allows you set set the relative phase to intermediate values, resulting in additional interesting dynamic shapes. Further controls are obvious.
This phenomenon, “Tusi Motion” was developed by Arthur Shapiro and Axel Rose-Henig, entered into the 2013 Illusion Contest, and deservedly received a prize. So why “Tusi”? Nasir al-Din Tusi, a 13th-century Persian astronomer, showed how to create a straight line from circular motion (so just the other way around, see the Tusi manuscript reference below).
The authors appropriately refer to a number of previous similar versions, going back a century. Arthur sent me some, and I'll add them here later.