
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.
 