Mathematics · Study 056
Maurer Rose
Connect 361 points on a rose curve, stepping d degrees at a time, and a Maurer rose appears. Slide d with your pointer to morph it.
What you're looking at
The bright outline is a rose curve, r equals the sine of n times the angle. The thin lines join points on that curve taken at angles 0, d, 2d, 3d and so on, in degrees. Because the chords skip around the rose, they weave polygons and stars whose form depends delicately on d.
The idea behind it
Peter Maurer introduced these figures in 1987. Most values of d give a dense tangle, while those sharing a factor with 360 collapse to a simple closed polygon. Sweeping d continuously, as here, passes through all of them and shows how abruptly the pattern reorganises.
Try this
Move the pointer left and right to choose d from 1 to 179 degrees. Click or tap to change the number of petals.
