movie The movie is in .mov format; about 2.8 Mbyte.
A movie of the algorithm running can be helpful in understanding how it works. This movie comes from joint work between myself and Paul Bourke, with my data and Paul's movie-making.
This is a simple square fractal. The color is log-periodic, i.e., the color changes in proportion to the logarithm of the circle radius. The color runs through one complete period, with the first and last colors the same. In such a scheme same-size squares have the same color. There is a tendency for the long gaps between large squres to fill up at about the same time.
One object was to demonstrate the space-filling property. To this end a c value close to the upper limit was used, resulting in a final image with 95% fill. A total of 3,432,618 trials were made to place 1001 squares, for an average of about 340 trials per placement. c=1.48, N=2.5, fractal D=1.35.
A mathematical account of the algorithm is given in the Shier-Bourke paper in Computer Graphics Forum: paper