For this image, one critical point was iterated but if it converged to a finite attractor, the other critical point was iterated. If it went to the same one, the phase difference was used in the coloring; the two might land on the same point of the attractor at the same time, or they might end up chasing each other around the attractor always separated by some number of points. This "distance" determines the colors of the petals of the flowers, which are found inside a period-7 "ghost bud" (which in an image using the second critical point as its "main" one would be a normal bud filling the screen).
Two of the five layers color divergent points (green) and points convergent to zero (blue). A third colors points converging to other attractors. All use smoothed iterations. Two further layers modify that third layer: one iterates both critical points and uses the phase difference and HSL addition to modify the hue; the other iterates both critical points and applies a shiny red coat of paint to the parameter points for which the dynamics have the maximum of four attractors. This last layer is barely visible; you can find a mini Mandelbrot near the bottom of the image that uses it.
Since there are five layers, and two of them iterate two critical points in tandem, there are seven full iterations per "inside" pixel here, so the speed is similar to a single-layer image with areas needing up to 9800 iterations. That doesn't sound too bad, except that this image also needed aggressive antialiasing. So instead of 2048*1536 pixels being calculated, 81 times as many sub-pixels were calculated. With up to 9800 iterations each. So over 800,000 iterations for a single pixel in all the higher-iteration parts of this image. Ouch!
Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.
Detailed statistics:
Name: Flower Power II
Date: February 11, 2009
Fractal: Antimatter (Herman Ring) Mandelbrot,
c-plane
Location: angle parameter ~=
phi (0.61803398), north-east area
Depth: Shallow
Min Iterations: 55
Max Iterations: 1400
Layers: 5
Anti-aliasing: 3x3, threshold 0.0, depth 2
Preparation time: 1 hour
Calculation time: 1 day (2GHz dual-core Athlon XP)