1. ) Euclid knew that every triangle, square, rectangle, circle or regular polygon has a center. ( center of gravity )
2. ) Euclid knew: If A. and B. be any two given points, there is one point C. who’s distance from A. and B. is equal. ( i.e. we can divide any line in half. )
3. ) Where ever two lines cross they meet at a point. ( howdy )
Happily, this is all the geometry an artist or designer needs to master dilation design space.
Any given space.
Teaching dilation strategy to others I have observed an almost universal inclination to refer to dilations as grids. The difference between dilations and grids is important enough to labour a bit. Most certainly dilation strategies are not grids and function more like a “warp engine” than specific increments of divided space extended out on a flat table. Increments, right angles and flatness are not prerequisites but, dilations can when needed supply grids of any desired metric or granule units of any size. Dilation strategy then doesn’t bother to pre-organize space, but rather assumes any given space to be a perfectly acceptable space to design in. Any given space can be self incremented by dilation. The difference then, rather than making designs fit a particular grid, grids, when you want them, are derived for a particular design space.
The Euclidian grid, being infinitely extend did not come with a system of proportion built in and so many artists and designers over the years sought out many different ways of introducing harmony into their works. Divine proportion being sometimes taught at design / art schools is only one of the better known systems. Though many graduates, in fact, still have difficulties with the “golden mean.” The golden spiral when employed by trees seems to give exceptional results, however, it doesn’t always produce good results when applied by designers. The divine spiral is singular and trying to apply it in all design work is a bit like trying to construct a forest by repetitions of single tree branch. It could to look odd. Only one of the many benefits of dilation strategy, on the other hand, is that dilations are constructed entirely of harmonious spirals should you need them. Always available when you want them and completely invisible when you don’t.
Dilation Design Strategy
From the stone age to yesterday and certainly tomorrow.
Dilation strategy being employed around the world since at least the stone age, in one way or another, is an essential part of new developments in imaging software but, for reasons I can only speculate of, was not researched or developed for class room use. Art and Design foundation teaching still relies on a profusion of disparate methods developed within specialized fields for seemingly different goals. Although almost all of the principles of dilation as a strategy could be, by the fourteenth century, observed in perspective drawing, that technology fixed it’s focus on “imitating reality” and remained a somewhat cumbersome specialized field. That dilation could be usefully employed as a comprehensive design strategy on it’s own merit escaped notice. Johannes Itten (November 11, 1888 – May 27, 1967) perhaps came closest to dilation as a comprehensive strategy while at the Bauhaus 1919 – 1922; though his process was intuitive, he made no specific writen reference to dilation and his construction methods were not self referring. Still, when I see some of his works I can’t help thinking he was grasping for a comprehensive strategy.
