I would like to graph these. But I am technologically challenged. Would anybody graph these interesting surfaces.
What is going on? This is an illustration of something called Picard's theorem. Which would say that no matter how small you draw a circle around the surface will take every single value possible! Try it, draw the circle . Inside this circle takes on every single value.
What is going on? This is an illustration of something called Maximum-Modulos theorem. Which would say that no matter where you draw a circle the maximum value on that region is attained on the boundary, never inside! Try it. And in fact for any irregular shaped closed curve. Take for example, on this ellipse the maximum value is on the boundary.