Parametric curve 2

The figure is one parametric curve drawn for t in [−c, c], then rotated four times by 90° to form a symmetric rosette.

x(t) = a · sin²(−b·t) · 2cos(cos(9.844·t))
y(t) = a · sin(sin(−b·t)) · cos²(9.844·t)

The inner frequency 9.844 = 4.28 × 2.3 is fixed here; its generalized sibling exposes it as a slider. Colour encodes distance from the origin: warm and bright at the centre, cooling and dimming toward the rim. Animate sweeps bbbb up and down around its current value.