Five cusps, like a buttercup, from a small wheel rolling round a big one. Five circles bring it within 1%.
Measuring the shape…
x = 6 cos t − cos 6t, y = 6 sin t − sin 6t
Named after the buttercup (Ranunculus). It is the epicycloid with five cusps: the rolling circle is a fifth the size of the fixed one, so it turns five times on the way round. One big circle carries almost the whole shape; the next ones carve the cusps.
Each path of the ranunculoid is traced by a chain of circles, each one spinning on the tip of the one before. A Fourier transform measures the path and works out every circle's size, speed and starting angle. The circles are sorted biggest first, so the first few give the rough shape and the rest add detail.
"Within 1%" means the drawing is, on average, less than 1% of its width away from the real outline. The bars show the circles of the main outline: height is size, position is how many times it turns per loop and in which direction. Click a bar to remove that circle and see what it was doing. Learn how it works.