(click the image for larger size)
Mandelbrot explains the construction in the book
Multifractals and 1/f Noise on page 126.
Start with generators: six circles, each tangent to
four of the others. (Shown below in black.)
The IFS to generate the fractal consists in six maps, inversions in these six circles. In the first picture above, the fractal is the non-colored (white) part of the picture. The limit points of each of the colors shown.
A faster way to generate the picture is also described. Start with an osculating base of eight disks, each with bounding circle orthogonal to three of the generators and not meeting the other three generators.
Color the disks in up to eight colors. Here, four are colored black, including the outside of the largest circle. Then apply the maps of the IFS to them repeatedly. These image disks fill the complement of the fractal.
