Alain’s curve

From mathcurve.com : Alain s curve (studied by Alain Juhel) is the projection of the intersection of the elliptical cone c²z²=a²x²-b²y² with the hyperbolic paraboloid cz=x²-y² onto the xy plane: So it makes sense to plot that xy projection as 0-level contour plot of a 3D surface. The equation (x² y²)² = a²*x² + b²*y² means plotting the zero level of f(x,y,a,b) = (x² y²)² = a²*x² + b²*y². Here s a…