I've just spent about an hour analysing photographs of Ely Cathedral.

You know what? Whoever designed that thing knew a crapload of stuff 
about geometry!

There are regular polygon prisms, cylinders and torii, circles, arcs, 
recursively nested epicycloids, curves and spirals, points and spires, 
shapes nested within shapes nested within shapes... The level of detail 
is astonishing. Every single individual archway has at least a dozen 
ribs to it. Every column has multiple pillars, and where column meets 
arch, there are disks and trapiziods and flowery scrolls. There are 
bicylindric vaults everywhere, some of them with hexagonal recursive 
ribbing, the ribs multi-loped and the crossings capped by guilt-painted 
flower buds. Even the gaps in the choir screen contain holes within 
holes, windows within windows, arches capped by spires surrounded in 
spires capped with smaller spires, beadwork everywhere...

I was going to try to moddel some of this stuff in POV-Ray, but I don't 
know - how much RAM does it take to describe 25 arches when each one is 
made up of four-dozen torii segments? How many CSG operations is that? 
The number of intersection tests per ray would be absurd...

My head hurts.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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