In the atlases below, I use the image of each fractal to show where the search found high-scoring locations. Each multibrot shares its atlas with its Julia sets: locations found on the base fractal are shown in blue, and values of c whose Julia sets held beautiful locations are shown in red. Where many wallpapers were found close together (the seahorse valley, for example), the atlas picks one to show.
Any interesting region of these fractals holds infinitely many small copies of the whole set, so a patient enough search could find a good picture almost anywhere. What's below is just what my search happened to find. Hover over a mark to see its pictures above the atlas, and click one to jump to its location in the fractal explorer and explore the area around it.
The atlas runs live here: a plate for each plane, marked with the places the search kept. It needs scripting, and a page served over the web rather than opened from a file. Open the atlas in the fractal explorer.
The Phoenix atlas only shows the Ushiki constants. The Phoenix fractal has more than one parameter, and the Phoenix plane in the fractal explorer lets you explore the others.