Happy Birthday Carina

A mathematical dance of flowers and wings, just for you.

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The Mathematics of Beauty

The swirls are generated using parametric Harmonograph equations:

$$ x(t) = A_1 \sin(f_1 t + p_1) e^{-d_1 t} + A_2 \sin(f_2 t + p_2) e^{-d_2 t} $$ $$ y(t) = A_3 \sin(f_3 t + p_3) e^{-d_3 t} + A_4 \sin(f_4 t + p_4) e^{-d_4 t} $$

Where A is Amplitude, f is Frequency, p is Phase, and d is Damping (friction).