Easily mistaken for the infinity sign, a circle, or any number of more complex pretzels and knots, the Lissajous figure is a picture of compound harmonic motion named for French physicist and mathematician Jules Antoine Lissajous (1822–1880). The shape is drawn by plotting a two-variable parametric equation as it iterates itself over time — the resulting figure is the picture of two systems falling into and out of phase.

These two varying signals produce a perpetual infinity (figuratively and literally as it will actually construct itself in the shape of the infinity sign given the right initial values). Any figure may be transformed into any other figure as the oscillating sine waves pass in and out of harmonic resonance.

Launch Jules. Double tap the screen of your device and move your finger up or down to change the speed at which Jules draws. Double tap again to hide the speed. By randomising the constants of the Lissajous curve’s equations, it draws a new shape every two minutes.

Swipe the screen with two fingers to start drawing a new figure. Tap and hold at any time to save a screenshot to your camera roll.

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iOS App, v8.0+