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)^{p}, k), k = 0, d, 2d, 3d, ..., 360d with the natural number d ≥ 1 (angle in degrees),
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)