2.17 Quartic Mandelbrot/Julia
(type=mandel4/julia4)
These fractal types are the moral equivalent of the original M and J
sets, except that they use the formula Z(n+1) = Z(n)^4 + C, which adds
additional pseudo-symmetries to the plots. The "Mandel4" set maps to the
"Julia4" set via -- surprise! -- the spacebar toggle. The M4 set is kind
of boring at first (the area between the "inside" and the "outside" of
the set is pretty thin, and it tends to take a few zooms to get to any
interesting sections), but it looks nice once you get there. The Julia
sets look nice right from the start.
Other powers, like Z(n)^3 or Z(n)^7, work in exactly the same fashion.
We used this one only because we're lazy, and Z(n)^4 = (Z(n)^2)^2.