This is a kind of unusual question, but I am pretty sure the function in this contour plot has an analytic form. I just don't remember what it was.
I found it in Stephen Boyd & Lieven Vandenberghes book (figure 3.2 page 113), but there seems no formula given.
Does anybody know what function this is? I would also help to know the formula for a function similar to this.
The paper Determining an Aesthetic Inscribed Curve describes how to generate smooth convex curves from convex polygons (Voronoi cells in that paper). It describes both implicit and parametric formulations. Here is a sample image from that paper: