Sin·cos abstract curve

Four copies of one parametric curve, rotated 90° apart about the origin, form this rosette. Each point is a radial envelope multiplied by two angular terms:

x(θ) = r·(1 − sin((b/c)·θ + φ))·cos((d/e)·θ + fΔ)·cos θ
y(θ) = r·(1 − cos((b/c)·θ + φ))·sin((d/e)·θ + fΔ)·sin θ

The ratios b/c and d/e are the modulation frequencies — coprime integers close the curve, while other ratios weave dense Lissajous-like webs. The phase φ sweeps 0…2π in steps of a·Δ, drawing a stack of envelope curves; f shifts the angular phase by f·Δ. The finished rosette rotates slowly about the origin.