This demo shows the three slice surfaces of the function `f(x,y,z) = x`^{2} - y^{3} + z^{5} at the hotspot `P`. In the "4D Color Graph" window, we slice the color graph by a horizontal `xy`-hyperplane and two vertical `xz`- and `yz`-hyperplanes and the slice surfaces are depicted in the corresponding 3D Graph.

You can rotate the slice surfaces around to see how the color of point `(x,y)` in the plane corresponds to the function value `f(x,y,z`_{0}). Move the hotspot around to look at the slice curves of different point in the domain.

Even though the hyperplanes appear as planes, they are really 3-dimensional objects: One of the three domain coordinates is fixed, and at each point, the fourth coordinate is free. Thus, any point in the `xy`-hyperplane can take on all possible colors.

Finally, the "All Slice Curves" window shows how the hyperplanes intersects the function graph: at each point `f(P)` in the intersection set with the function graph, we get the color that the function graph has at `P`.