A pattern drawn by a pen as a small circle rolls around inside a large one. Change the radii and pen position with sliders and see how the number ratio changes the pattern's shape.
A spirograph is a toy that draws a pattern with a pen by rolling a small toothed circle inside a large circular frame. The pattern's whole appearance is decided entirely by the ratio of the two circles' radii. Call the large circle's radius R and the small circle's radius r, and reduce that to the simplest whole-number ratio (for example, R:r = 24:7) — the smaller number (7) becomes the number of petals in the finished pattern.
When R and r share a large greatest common divisor, the pattern stays simple; the closer the two numbers are to coprime (sharing almost no common divisor), the more revolutions the small circle needs to make, producing a denser, more elaborate pattern. Where you place the pen matters too — closer to the small circle's edge gives pointed shapes, closer to the center gives rounder, petal-like shapes. Change the radii and pen position with the sliders and see how the pattern changes.