Plotting a Four Dimensional Function
This animated plot shows a sequence of three dimensional “slices” of a four dimensional function. The function is f(r,s,t) = r^2 * s^2 * t^5. r and s are each given a range of -1 to 1. f(r,s,t) is plotted from -2 to 2. t is varied from -4 to 4. For a given value of ta three dimensional plot is displayed. t is animated (varied automatically) with values from -4 to 4 giving a series of three dimensional plots that yield an animation of the three dimensional slices of the four dimensional function. This animation was produced using Mathematica 6 from Wolfram Research. Mathematica 6 provides the ability to “manipulate” and “animate” parameters to create interactive and animated graphs. The change in viewpoint was accomplished by “grabbing” the graph with the mouse and dragging it. The video was produced by using Snapz Pro X (from Ambrosia Software) to do a screen capture while using Mathematica on a Mac OS X computer. The Animate and Plot3D functions were used in Mathematica to achieve the graph shown.