The five easy steps to a 0.5 dilation space 1, 2, 3, 4, and 5.
A, B, C, and D are simply repeats/iterations of steps four and five.
The same process can be applied to any rectangle.
Harmonics below.
Page spreads are discussed here.
Text columns and their spacing, though not necessarily obvious above, are handy work within a page dilation. I’ll provide a few “text book” examples below and expect that creative folk will come up with many more on their own. Any dilation will reflect the proportions of the original design space or page.
There are 6 “self similar” rectangles below of which 4 of the central smallest (3,4,5,6,) can be used to propoationally space text columns and page elements.
Orange dots indicate the two column centers.
For this four column layout next the footer is a fifth iteration, the header remains the same (3) as above and the spacers are sixth. The columns layout in the spaces between the orange dots.
A three column layout is a slightly different proceedure, because, we first need to locate page thirds.
Step one: locate these three points at A below.
Step two: conect the “dots” as in diagram B.
A. 
B. 
These new lines cross the Z axis and divide the page into three equall parts at C.
C. 
and 
Having located page thirds and laid out columns with a “fifth” spacer we can now see an even easier way.
Our three column width very nearly matches a third iteration spacer or exactly 1/4 of the page width. If then, we take the third iteration to be our column width and the fifth to be column spacers we can dispense with the ritual of finding page thirds and simply layout the three column page. A six column page if we want.
Knowing how to find page thirds is also handy for folding stock or brochures etc…
Allen Patten
