Rectangular Coordinate Transformation

The first entries are rotation values around the X, Y, and Z axes. Think
of your starting image as a flat map: the X value tilts the bottom of your
monitor towards you by X degrees, the Y value pulls the left side of the
monitor towards you, and the Z value spins it counter-clockwise. Note that
these are NOT independent rotations: the image is rotated first along the
X-axis, then along the Y-axis, and finally along the Z-axis. Those are
YOUR axes, not those of your (by now hopelessly skewed) monitor. All
rotations actually occur through the center of the original image. Rotation
parameters are not used when a ray tracing option has been selected.

Then there are three scaling factors in percent. Initially, leave the X
and Y axes alone and play with Z, now the vertical axis, which translates
into surface "roughness."  High values of Z make spiky, on-beyond-Alpine
mountains and improbably deep valleys; low values make gentle, rolling
terrain. Negative roughness is legal: if you're doing an M-set image and
want Mandelbrot Lake to be below the ground, instead of eerily floating
above, try a roughness of about -30%.

Next we need a water level -- really a minimum-color value that performs
the function "if (color < waterlevel) color = waterlevel". So it plots all
colors "below" the one you choose at the level of that color, with the
effect of filling in "valleys" and converting them to "lakes."

Now we enter a perspective distance, which you can think of as the
"distance" from your eye to the image. A zero value (the default) means no
perspective calculations, which allows use of a faster algorithm.
Perspective distance is not available if you have selected a ray tracing
option.

For non-zero values, picture a box with the original X-Y plane of your
flat fractal on the bottom, and your 3D fractal inside. A perspective
value of 100% places your eye right at the edge of the box and yields
fairly severe distortion, like a close view through a wide-angle lens.
200% puts your eye as far from the front of the box as the back is behind.
300% puts your eye twice as far from the front of the box as the back is,
etc. Try about 150% for reasonable results. Much larger values put you far
away for even less distortion, while values smaller than 100% put you
"inside" the box. Try larger values first, and work your way in.

Next, you are prompted for two types of X and Y shifts (now back in the
plane of your screen) that let you move the final image around if you'd
like to re-center it. The first set, x and y shift with perspective, move
the image and the effect changes the perspective you see. The second set,
"x and y adjust without perspective", move the image but do not change
perspective. They are used just for positioning the final image on the
screen. Shifting of any type is not available if you have selected a ray
tracing option.