TITLE: Moorish Geometric
NAME: Samuel J. Goldstein
COUNTRY: The country you are a citizen of
EMAIL: libelle@webbwerks.com
WEBPAGE: http://www.cyberverse.com/~meander
TOPIC: Math & Physics
COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT.
JPGFILE: moor.jpg
ZIPFILE: moor.zip
RENDERER USED: 
    POV-ray 3.01

TOOLS USED: 
    Paper & Pencil

RENDER TIME: 
    3 hours 45 minutes 46.0 seconds

HARDWARE USED: 
    SGI Indigo2/150

IMAGE DESCRIPTION: 

Geometry is the mystical place where mathematics becomes Interesting.

This is another tip of the (virtual) hat to the anonymous Islamic
artists of ages past, who did beautiful, complicated things using
simple geometric rules.


DESCRIPTION OF HOW THIS IMAGE WAS CREATED: 

I wrote in the notes for geo.pov that I wasn't able to make it work
programmatically. Well, I decided that the general case was too general,
and special-cased the iteration portion. So it DOES work in a limited
sense.

The geometrical "rule" is as follows:
This basically starts with a 30-60-90 triangle, which is then
algorithmically flipped and inverted to make a 120-30-30 triangle.
Three of these are combined to make a 60-60-60 triangle. These are
combined to make hexagons. Then these are tiled out to form the
rosettes.

This technique can be used to create an infinite number of intricate
geometrical patterns, many of which are quite pleasing.

When using moor.inc, remember that your base triangle is between the
points <0,0,0>, <1,0,0>, and <1,0,1.7320508>. Any object crossing the
lines between these points should do so at y=0 for a continuous pattern
to be made.

If this doesn't make sense, feel free to email me. I can't promise that
I can verbalize it clearly, but I'll try 8*).