Mike, Excellent images (has anyone called you "the new Paul W. Carlson" already?) Regarding the Epicycloid_Mset formula: Replacing the line "ang=atan(imag(w)/real(w)" with "ang=imag(log(w))" will remove the restriction of having to use only even numbers of cusps, since the complex log() utilises atan2() internally. And my 2 cents on the inverted looking Astroid curve "issue": Curve formulas in parametrised form generally are not identical with those of the same curve in polar form. The parameter is a kind of yardstick along the curve and might be mistaken for the polar angle because of all the trigonometric function that pop up in parameter formulas, but most of the time it is not - and often it will no even be possible to transfer a parametric to a polar expression in closed form. Of course I'm aware noone (including me) will complain if something looks good but is not quite correct, just wanted to point it out (SIWOTI syndrome maybe?) For this not to be completely useless - there *does* exist a polar formula for the Astroid. Replacing the lines ang=atan(imag(w)/real(w)) astroid=r*(cos(ang)^3+i*sin(ang)^3) with ang=imag(w)/real(w) ;ang is really tan(ang) here astroid = r * sqrt((ang^2 + 1)/(|ang|^(1/3) + 1)^3) will produce "uninverted" Astroids. Gerald