r = sin(n ⋅ θ)^{p} describes the rose for the first variant in polar coordinates with n ≥ 1 and p ≥ 1,
points on the rose: P_{k} = (sin(n ⋅ k/z)^{p}, k), k = 0, d, 2d, 3d, ..., u ⋅ d with the natural number d ≥ 1 and the maximal number of points u, z subdivides the circle instead of the usual 360.

You can also try values like z = 359.999, n = 45, d = 261, giving figures like this: (.svg)/(.pdf)