in news:3CF23169.FF4E9361@reading.ac.uk Michael Andrews wrote:

> Well, this one is easy :-)

Yeah, right.

> [...]
> #declare fn_Rad = function { pigment { radial colour_map{[0 rgb 0][1 rgb
> 1]}} }

Replacing radial by cells also gives a nice result, with other patterns it 
looks more like prepared rat organs under a microscope. 

Thanks,

Ingo

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Hi Dennis,

Dennis Miller wrote:
> 
> That's really sharp. I am trying to turn that into a function for an
> isosurface but am having some trouble. Might you assist?
> Dennis
> 

I don't think you can make a sensible isosurface of it - each cusp
represents a discontinuity in the function and isosurfaces tend to give
up and sulk at that point ...

Mike Andrews.

PS: changing fn_Cusp to ...

#declare fn_Cusp = function {
fn_Rad(f_snoise3d(x/2,0,z/10),0,f_snoise3d(x/10,100,z/2)).x }

... makes a nice wet-on-wet watercolour varaition.

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Xns### [at] povrayorg...

> Just a nice function to play with, vary the floats A-L.

Hey, it looks a lot like the family of functions I played with when I first
used isosurfaces some years ago. I used the best ones in this image :
http://www.oyonale.com/ldc/english/reading.htm

I recently tried to convert the old iso code to Povray 3.5 with moderate
success but I could try harder and make them available. They are still the
coolest thing, particularly when animated.

G.


--

**********************
http://www.oyonale.com
**********************
- Graphic experiments
- POV-Ray and Poser computer images
- Posters

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On 25 May 2002 18:08:09 -0400, ingo wrote:
> And this as an inspiration for Ron:
> http://glinda.lrsm.upenn.edu/~weeks/software/quasic.html

I'll bet you all thought I was dead.

This is pretty, but unfortunately the algorithm he describes doesn't seem to 
lend itself to arbitrary evaluation like we need for procedural textures.

However, it seems to be related to the fact that a Penrose tiling is the
projection of a 5-dimensional lattice onto a 2-dimensional plane with a
specific rotation with respect to the lattice.  For a procedural texture, of
course, one might choose instead to use the projection of a 5-dimensional
lattice onto a 3-dimensional space.  

--
#macro R(L P)sphere{L __}cylinder{L P __}#end#macro P(_1)union{R(z+_ z)R(-z _-z)
R(_-z*3_+z)torus{1__ clipped_by{plane{_ 0}}}translate z+_1}#end#macro S(_)9-(_1-
_)*(_1-_)#end#macro Z(_1 _ __)union{P(_)P(-_)R(y-z-1_)translate.1*_1-y*8pigment{
rgb<S(7)S(5)S(3)>}}#if(_1)Z(_1-__,_,__)#end#end Z(10x*-2,.2)camera{rotate x*90}

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in news:slr### [at] fwicom Ron Parker wrote:

> On 25 May 2002 18:08:09 -0400, ingo wrote:
>> And this as an inspiration for Ron:
>> http://glinda.lrsm.upenn.edu/~weeks/software/quasic.html
> 
> I'll bet you all thought I was dead.

and buried under a load of code..

> [...] one might choose instead to use the
> projection of a 5-dimensional lattice onto a 3-dimensional space.  

What would the result look like? Would every single tile take a limited 
amount of 3d space instead of being streched to infinity along one axis 
(like the hexagon pattern). Would it tile/tesselate in all 3 dimensions?

Ingo

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On 7 Jun 2002 03:40:24 -0400, ingo wrote:
> in news:slr### [at] fwicom Ron Parker wrote:
> 
>> On 25 May 2002 18:08:09 -0400, ingo wrote:
>>> And this as an inspiration for Ron:
>>> http://glinda.lrsm.upenn.edu/~weeks/software/quasic.html
>> 
>> I'll bet you all thought I was dead.
> 
> and buried under a load of code..
> 
>> [...] one might choose instead to use the
>> projection of a 5-dimensional lattice onto a 3-dimensional space.  
> 
> What would the result look like? Would every single tile take a limited 
> amount of 3d space instead of being streched to infinity along one axis 
> (like the hexagon pattern). Would it tile/tesselate in all 3 dimensions?

Yes.  They'd be something like the crackle pattern, but with a stronger
appearance of periodicity.

See http://www.cmp.caltech.edu/~lifshitz/quasicrystals.html for the real-life
version, and http://www.geom.umn.edu/apps/quasitiler/about.html for the math.

-- 
#local R=rgb 99;#local P=R-R;#local F=pigment{gradient x}box{0,1pigment{gradient
y pigment_map{[.5F pigment_map{[.3R][.3F color_map{[.15red 99][.15P]}rotate z*45
translate x]}]#local H=pigment{gradient y color_map{[.5P][.5R]}scale 1/3}[.5F
pigment_map{[.3R][.3H][.7H][.7R]}]}}}camera{location.5-3*z}//only my opinions

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