However, the iterated exponentiation of complex numbers creates its own complex Universe filled with stars, galaxies, and their clusters. To see them, you just need to plot in the complex plane one point per iteration. Those who have solved the present problem remember that searching the z plane for interesting values, which create objects of intriguing shape, glued them to their computer monitors for hours. Let us first take a look at the first three out of 6 objects in the picture below. They correspond to the points in the z plane along the imaginary axis.
Some galaxies have spiral arms about that tightly wrapped.
The still 3-armed spiral got even tighter, and now our object resembles a warped disk of a galaxy. Again, this is not the most common bi-symmetric warp but we haven't really been looking for such here. Next, consider in the above figure the remaining 3 objects obtained by following a line in the complex plane parallel but offset by unity from the imaginary axis. The almost-radial symmetry involved in the picture is misleading, however. Unfortunately, in real galaxies of this type the arms are not so regular and continuous throughout the galaxy.