A tangent circle for every fraction, sitting on the number line with a radius of one over twice the square of its denominator — and two circles touch exactly when their fractions are Farey neighbours, so the picture is a proof; the depth follows the level and the mediants appear between.
Drawn with: a WebGL2 shader.
Reacts to and looks like: gpu, webgl2 and audio-reactive.
Family: Visualiser.
Runs in your browser. The preview above is the same program the renderer uses.