The process of quaternion mapping in a nutshell (how I do it): Once you know how to calculate quaternion functions (like c^q), any formula will do. Not all formulas produce esthetically-pleasing images, but the process of mapping them is the same for all formulas. You iterate a formula with varying x, y and z coordinates for each pixel until you find the border of a quaternion island, if it exists, or until you reach the limits of your exploration depths. (Any point where the iteration doesn't "blow up" is considered inside a quaternion solid.) Then you go back with finer steps until you enter the quaternion island again. For each pixel you save the location of the q-border in a z-buffer for ray-tracing later. The ray-tracing algorithm calculates the pixel's palette index, light and viewing angles, and Phong highlights, given the pixel's location in the bitmap and its z-depth. There is the chance that some details may be missed if the quaternion has a depth greater than the depth explored, or if the image is particularly fragmented, or has hollow spots in its interior. So one option to reveal more details inside a quaternion is to "dive" into the island(s) and strip away layers. This works like a "slicing" process without the knife edge.