Dynamic Geometry, Mathematical Art, and Geometric Algebra

Now for some history on how playing with Geometry led me to Mathematical Art, and that led to Geometric Algebra, and so to creating Algorithmic Beauty Software and this blog.  If you haven't yet read my previous post on "The Geometry of the Many-Angled Ones", please follow that link and read it; there's a very basic description of Geometric Algebra there, and that's the basis of the software I'm designing. When you come back, jump past the cut for the rest if this post.

A Geometry for the Many-Angled Ones

The title of this post is taken from the science fiction of Charlie Stross, a British writer living in Scotland, and specifically his "Laundry Files" series.  The Laundry is a highly-classified British Intelligence and Counter-Espionage agency whose primary brief is the protection of the United Kingdom against the depredations of evil extra-dimensional beings who wish to invade, possess, destroy, and otherwise prey on humans and their world.

The basic conceit is that H. P. Lovecraft's writings are true: there are beings of great power lurking just around the corner in a higher-dimensional multiverse, beings who can be called forth using forms of geometry and computer software.  In the world of the Laundry, Alan Turing didn't just invent the mathematical underpinnings of the theory of computation; the secret part of his work that the rest of the world didn't get to see shows how mathematics and computer programs can be used to do what amounts to "magic".  Stross' hero, Bob Howard, is a middle-echelon IT sysadmin and secret agent, recruited into the Laundry just before his university computer graphics project could invite in beings that would have leveled the city of Wolverhampton¹.

Algorithmic Beauty Software and this site are the result of some research I've been doing in modern geometry in the couple of years.  One of the subjects I've been studying intensively is a field called "Geometric Algebra"² which just might be the geometry that Lovecraft's "Many-Angled Ones" use in navigating their sinister travels through the universes. I'll explain more after the cut.  Don't be too bothered by the mathematical terms; I'll try to summarize the meaning of it all so you won't have a mathematician to get it, and for those who are interested in the details, I'm planning to write some more posts in the near future that will dive into them. And I'll try to avoid gaining the attention of the Great Old Ones and getting eaten by them before I finish.