Some of these are off the net. Most are quaternion sets I did myself. All illustrate the principle that complex behavior can result from the iteration of a simple system. All the source code can be found here.

See also Henrik Engström's quaternion theory page.

Some 2D slices of 4D quaternion Julia sets.

, 78K. , 138K. , 83K. , 28K.

, 216K. , 121K.

David Engström did this one: , 162K, and this one: , 81K.

These remind me of plants: , 158K. , 46K.

Here's a pair of images that are the same fractal but with different
colorings:

, 354K.
, 303K.

Here's another pair that are the same but with different colors:

, 186K.
, 93K (nice one).

These are both real nice: , 159K. , 171K.

My very first quaternion: , 107K.

Some 3D slices of 4D quaternions, by Henrik Engström: quat006.gif, 319K. quat015.gif, 428K.

Miscellaneous: picasso.gif, 357K, from Noel Giffin's Spanky Fractal Database.

A coloring of the Mandelbrot set that looks like a seated Buddha. Click here for more info. , 152K, off the net.

These are Mandelbrot sets for a non-analytic 2D map:

, 163K.
, 101K.
, 273K.
, 303K.