|
Add two successive Fibonacci numbers such as 1, 2, 3, 5, 8, 13... and you'll get the next. The corresponding ratios 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34 ... converge to the harmonic proportion: 1/2 (square root of 5) - 1/2 = 0.618034... It divides 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. Let's use it to design web pages such as the one you are reading right now - compare examples to the right. Copyright notice (2005): Jürgen 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. Last update: October 2009. Original version of this page: 2005 |
|
Make web pages using the golden proportion and Fibonacci numbers! Like Professor Schmidhuber, whose web pages and talk slides are graphically structured based on these principles. . |
|
Top: Cut-out of Schmidhuber's home page and Cogbotlab page, scaled down by powers of the harmonic proportion. Blue lines indicate recursive applications of the golden ratio, approximated through Fibonacci ratios with a base length of 2 pixels. That is, we multiply Fibonacci numbers by 2 to obtain object sizes (e.g., image widths and heights) of 2, 4, 6, 10, 16, 26, 42, ..., 754 pixels. We do this because 754 pixels yield a fine display width for many screens, while the "most desirable" (most accurate, minimal) base length of 1 pixel does not. Text Margins. Once you have chosen a particular outline of your Fibonacci web design, such as the present 4 column page with column widths 178 / 288 / 178 / 110 pixels, additional design decisions are needed regarding the margins separating texts and other graphical elements. But don't agonize too long over how to select appropriate margin sizes! Schmidhuber's most elegant solution may be: no left margins for left-justified text; no right margins for right-justified text! Like in the present page, or the Cotesys page, or the STIFF project page, etc.
Note that certain artworks exploiting Fibonacci proportions are special cases of
Low-Complexity Art
based on the general
Theory of Beauty.
|
|
More examples of the type below: Robots Evolution Evo-RNN Resilience Curiosity Physics AI |
|
Above: individual graphical elements such as this one for the page on a New Kind of Empire should also follow the same fractal Fibonacci design rules whenever this is possible. Right: Alternative Fibonacci proportions for the Recurrent Network page and the Goedel machine page and others. Again, blue lines indicate recursive applications of Fibonacci ratios, this time using a much larger base length of 90 pixels. |
That is, above we limit ourselves to object sizes of 90, 180, 270, 450, 720 pixels (multiples of 1, 2, 3, 5, 8). Not as precise as the base length of 2 pixels used in the present page, but not bad either.