Swallowtail Bifurcation

This model represents the swallowtail bifurcation from nonlinear dynamics. It represents the equilibrium points of the non-linear system:
1.25(x/10)^6+ - 6 (x/10)^4 + 6(x/10)^2 + r(x/10) + 10h == 0
The axis are oriented as follows:
1) Place the object so the largest opening is toward the table.
2) Rotate it so it is possible to look under the model
3) The x-axis ranges from -20 to 20 horizontal and parallel to you. The r-axis ranges from -10 to 10 horizontal and moving directly away from you. The h-axis ranges from -0.5 to 0.5 and runs upward from the table.

Anyone familiar with dynamics, and especially non-linear dynamics knows how important the equilibrium points of a system are. The study of the locations of these points as the system parameters change is known as bifurcation theory. This surface is meant to provide a visual aid for students of nonlinear dynamics.

The 3D surface can be created in Mathematica using
ContourPlot3D[1.25(x/10)^6 - 6 (x/10)^4 + 6(x/10)^2 + r(x/10) + h10 == 0, {h, -1.5, .5}, {r, -10, 10}, {x, -25, 25}, MaxRecursion -> 15, PlotPoints -> 20, ContourStyle -> Opacity[.3], ViewPoint -> {0, 0, Infinity}, Boxed -> False]