TITLE: quasi crystals
NAME: Rob Wieringa
COUNTRY: The Netherlands
EMAIL: wieringa@natlab.research.philips.com
WEBPAGE: --
TOPIC: Physics & Math
COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT.
JPGFILE: pball.jpg
ZIPFILE: pball.zip
RENDERER USED: 
    povray 3.0

TOOLS USED: 
    penta (see below)

RENDER TIME: 
    2 hours 21 minutes 3.0 seconds (8463 seconds)

HARDWARE USED: 
    Sun Solaris SPARC5

IMAGE DESCRIPTION: 


 This image shows a plane of so called quasi-crystals: non-periodic 
 crystal-like structures in which 5-fold (almost) symmetric patterns 
 occur.

 The theory behind these crystals has been developed by Prof. N.G. de Bruijn
 "on top of" Penroses irregular tilings. See:
 "Algebraic theory of Penrose's non-periodic tilings of the plane", and
 "Quasi crystals and their Fourier transform", both in:
 Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen
 (Royal Dutch Academy of Science).
 N.G. de Bruijn developed this 3D extension after an idea I had, and 
 considered it as pure math (and math he used in the description!).
 After some time crystallographers found an application in physics, 
 when they noticed 5-fold symmetry signs in (Aluminium?) crystals, which
 was up to then considered to be impossible, or at least unlikely.

 The crystal surface consists of a quasi-regular pattern of rhombuses, 
 each having diagonals with golden ratio. 
 Using 30 of these rhombuses, the glowing "balls" were composed, 
 suggesting a kind of "emission" from the crystal's surface.
 

DESCRIPTION OF HOW THIS IMAGE WAS CREATED: 


 The generation of the plane (consisting of lots of rhombuses) is done
 with a special purpose program called penta.
 The original version of this program has been written in the eighties 
 by a student of de Bruijn (with my help) in ALGOL60, and generated plot 
 commands.
 Later (in the early nineties) I ported the program to C, and changed it
 to generate postscript.
 I "rediscovered" it some time ago, and changed it again to generate POV
 source. 
 With its parameter set to 5 (as I used in this picture), it generates a 
 file with 6568 rhombuses. I won't include that file (being more than 
 500.000 bytes) in the zip file, since it can be generated easily from the 
 included penta program.

 The rest of the picture's source is pure hand written POV code: 
 the look of the rhombuses, the "balls", and their glow. For textures
 I "reused" some of the stuff from the include files that come with POV.