Mandalas embody mathematical symmetry groups — specifically the cyclic group Cₙ of rotational symmetry. Each arm is generated by a parametric curve r(θ) = A·sin(pθ), where p determines the number of petals (rose curves). Lissajous figures arise when horizontal and vertical oscillations have integer frequency ratios, tracing closed curves when the ratio is rational. Layering multiple frequency components creates the intricate nested structure seen in traditional geometric art, all governed by the dihedral symmetry group Dₙ combining rotations with reflections.