🚀 go-pugleaf

Well, I attended a lecture once on fractal generation... it was quite
fascinating.  Here are some variants on the mandelbrot set:

z = z^n + c

In this case, n determines the number of major "lobes" that the Mandelbrot-like
set contains.  For n = 2, you get a normal M-set, with a "butt" (2 lobes).
You can also use fractional numbers for n instead of integers.  I've been told
n = 1/2 is rather boring to look at, and n = 1 is not a good idea either, but
n = pi might be interesting, or n = 1/e.

z = sin(z) + c
z = cos(z) + c
z = tan(z) + c
etc.

These all give fascinating repeating structures that have a Mandelbrot/Julia
set "feel" to them.  I can't really describe them too well, except to say
that the structures tend to repeat linearly in the direction of the real
axis (as you would expect from trig functions).

Equations for complex-number equivalents of the real-number trig functions are,
of course, available in the CRC math reference, but you can rederive them
from the exponential equation quite easily.

I am not sure how "pretty" or "interesting" the hyperbolic functions would be.

Rob Poole
pooler@rpi.edu
pooler@cs.rpi.edu