A map f:D2→D2 from the disk to itself has its graph living in D2×D2⊂R4. Restricting the domain to a circle of radius r gives a curve in the solid torus S1×D2. This program displays the graphs of f and the identity side by side: at r=0 the two curves are unlinked, but at r=1 they have linking number 1. Since the linking number must change continuously, the curves must cross at some intermediate r, producing a fixed point of f. A slider in the GUI controls the radius r.
Controls: Click and drag to orbit, scroll to zoom.
