Rhodonea curves r = cos(k*theta) produce rose-like shapes. When k = n/d (rational):
if n*d is odd, the rose has n*d petals; if either is even, it has 2*n*d petals.
Integer k=2 gives 4 petals, k=3 gives 3, k=5 gives 5 — but rational k opens up infinitely intricate families.
These curves were studied by Luigi Guido Grandi in 1723, who named them "rhodoneae".