Before Mathematica I never would have seen this graph! Notice, another spiral! (Actually there are 4 spirals here if you look at the endpoints of the segments). And notice that ii is a real number! Amazing stuff here. One of the finest math sites on the internet, which has interactive applets, is IES in Japan. One applet they made was inspired by the graph above, is under complex number i^(i^i..). You can drag the point at 0+1i around the complex plane to get some amazing things!! (You need to download Java (free) to see these).
See Chapter 11 Questions and answers.