Jürgen Schmidhuber (2005)		FIBONACCI WEB DESIGN			Making web pages using harmonic proportion and Fibonacci numbers
Many of Prof. Schmidhuber's web pages and talk slides (e.g., this one) are graphically structured through Fibonacci ratios and the `golden' proportion.		Background: The ratios of subsequent Fibonacci numbers: 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34 ... converge to the harmonic proportion 0.5*(square root of 5 - 1) = 0.618034..., dividing the unit interval into segments of lengths a and b such that a/b=b. Many artists claim the human eye prefers this ratio over others. (Low-complexity art is based on a more general theory of beauty.)			Applications (below): Cut-outs of home and cogbotlab page. Blue lines indicate recursive applications of the harmonic proportion, approximated through Fibonacci ratios with a base length of 2 pixels. That is, we multiply Fibonacci numbers by 2 to obtain object sizes of 2, 4, 6, 10, 16, 26, 42, ..., 754 pixels. This yields a fine display width for many screens, while the "most desirable" base length of 1 pixel does not.

Scroll down: Alternative Fibonacci basis for the Goedel machine page and others. Blue lines indicate recursive applications of Fibonacci ratios, this time using a much larger base length of 90 pixels. That is, we limit ourselves to object sizes of 90, 180, 270, 450, 720 pixels (multiples of Fibonacci numbers 1, 2, 3, 5, 8). Not as precise, but not bad either.		Copyright notice (2005): Schmidhuber will be delighted if you use the principles outlined here for your own web designs, provided you prominently mention the source and provide a link to the present page.