Parameter Plane of Exponential Map

The first three columns zoom into the line z=x+π i that corresponds to x<0 in the tetration fractal. The final column reflects the bottom half of the fractals from the previous column to the top half approximating a reflection around the imaginary axis of the star portion of the tetration fractal. By iterating a*e^z instead of a^z, dynamics can be explored that can't occur in the tetration fractal because it avoids the destruction of information caused by e^z+2^πik=e^z. See Robert Devaney's web site for more information about the exponential map and chaos in general.