This is my best effort to duplicate the image "Map 43" from "The Beauty of Fractals."
I've always liked the black and white images from that book, and finally found documentation on the method they used in the book "The Science of Fractal Images"
These images are generated using the "Distance Estimator Method" (DEM). I have my own take on this method, that uses a logarithmic (actually y=x^a) color scheme to create anti-aliased black and white images.
To get the clearest image possible I created the original at 4X resolution (3200x3200) and then down-sampled to 800x800 in Photoshop.
To recreate this plot at a lower resolution using FractalWorks 0.4.10, click here: B of F map 43 DEM