Subdivision Iteration Columns and You!

Doric. Ionic. Dear Abby. If you've studied architecture, particularly classic, you know all about and are probably very sick of columns. Yes, they are crucial to any building's structure, but how interesting could a cylindrical support be in a time when the traditional is being replaced by more organic, fluid, and expressive styles? The answer is very. But to get there, we need to make a quick stop in the land of geometry.
More specifically, the realm of subdivision. This is a vastly complex but completely amazing field, in which I cannot claim to have much knowledge. I do know some basics. Here's how it works: Using relatively simple mathematic formulas, a simple sphere or cube can be turned into an intricately beautiful form. This is done by repeatedly dividing the surface. A cube starts with 6 sides and is divided so that it has 36 sides. When subdivided again, it has 216, then 1296, then 7776, and so on. This process can be repeated infinitely, and with each step, the form becomes exponentially more complicated. You can tweak the formulas to change the number of sides, divisions, etc.. (This is very similar to the way snowflakes are formed). With little more than a modeling program and a formula, you can end up with something like these:

Architects are already looking to use this phenomenon on a large scale, but construction processes capable of making buildings as complex as the images above is still decades away.
But, we still have columns, and that's where. Michael Hansmeyer comes in. He's working in the fascinating world of computational architecture, and he's come up with a simple and elegant solution to our boring columns using only the theory of subdivision and a lot of paper. Instead of starting out with a cube or sphere, he begins his forms with a doric column. The already complex form is subdivided until it resembles something like this:

When he's finished, the column has 16 million facets. That's a lot. Too many, in fact, for any existing manufacturing technique to even attempt. So, to make his columns a reality, he had to turn to every computer nerd's worst nightmare: paper.

He took thousands of 1 mm cross-sections of the column and fed them into a paper-cutting computer, which then made identical physical copies of the cross-sections. These were stacked to finally form a physical column, like the ones in the pictures below. I think the beauty and potential speaks for itself. It's amazing to think that we can see the intricate future of architecture captured in its simplest form.