# Whitney Umbrella

Whitney Umbrella is the surface of this equation: “x^2-y^2*z == 0”. Note that the z-axis is part of the surface.

ParametricPlot3D[{u*v, u, v^2}, {u, -2, 2}, {v, -2, 2}, BoxRatios -> {1, 1, 1}, Axes -> False, Boxed -> False, BoundaryStyle -> {Thin, White}, PlotPoints -> 25, MeshStyle -> {RandomColor[], RandomColor[]}, PlotStyle -> Directive[RandomColor[], Opacity[0.9], Specularity[White, 30]]]

ContourPlot3D[x^2 - y^2*z == 0, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, PlotRange -> All]

m = 50; ContourPlot3D[x^2 - y^2*z == 0, {x, -m, m}, {y, -m, m}, {z, -m, m}, PlotRange -> All, Mesh -> All, Boxed -> True, Axes -> True, MeshStyle -> {Gray}, ContourStyle -> Directive[RandomColor[], Opacity[0.7], Specularity[1, 20]]]