This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
The Mandelbrot set being the most famous fractal, its various
regions are well known and many of them have popular names evoking
graphic details found by zooming into them. The seahorse valley is the
limit border of the main cardioid at the negative side of the x axis
(near to x=-0.75, y=0.0). You can see here convoluted and complex buds
looking more or less like seahorses. The elephant valley is near the
symetry plane on the positive side of the x axis (x=0.25, y=0.0).
Spirals protuding from the border evoke trunks of elephants. By
zooming in these regions many interesting structures can be seen.
A nice guide (by Paul Derbyshire) to explore the various regions of
the Mandelbrot set can be found at :