Quartic Surface for Contours

cults3d

I created this quartic surface in Wolfram Mathematica for printing with contours at equally spaced intervals in the z-direction to have a nice model to share with my students when I teach surfaces and contour maps. The equation of the surface is z = 2 x^2 - x^4 - 2 y^2 + y^4 and it works well for illustration since it has local maximum and minimum points as well as multiple saddle points. I often find myself teaching about 3D printing while teaching about contours and level sets. I set up the print for this model with Simplify3D and 21 processes at appropriate intervals to achieve the look I wanted. My model was printed with full supports throughout. I tried with fewer supports but did not have success. Also included is a "Boundary Frame" model. I used this short square in my print to help make the ooze shield have straight edges which speeds up print time.