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In the equations for Starr curves with four parameters a, b, c and d sin b t is now replaced by cos b t so instead of x(t) = ( d + sin a t ) cos(t + (sin b t ) / c) y(t) = ( d + sin a t ) sin(t + (sin b t) / c) I have used x(t) = ( d + sin a t ) cos(t + (cos b t) / c) y(t) = ( d + sin a t ) sin(t + (cos b t) / c) I call these curves 'Starr curves' because mathematician Norton Starr came up with the idea of using this kind of curves for creating computer graphics (see Stan Wagon: Mathematica in Action).