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"Mr Seb" <ban### [at] wanadoo fr> wrote:
> Nice !
> The penrose floor is nice. Interesting code !
>
> news:web.447078752a55f1ca1039d0950@news.povray.org...
> > Nifty! Thanks.
> >
> > "PM 2Ring" <nomail@nomail> wrote:
> > > Here's one of the Kepler-Poinsot solids: the small stellated
> dodecahedron,
> > > on a Penrose tiling floor. The code also contains a slightly simpler &
> more
> > > accurate dodecahedron than the one in the shapes2.inc.
> > >
> > > Enjoy!
Thanks, guys! I had a clear one with dispersion and area lights going all
weekend and half of Monday on my machine at work... I've *got* to do one
with photons, radiosity and maybe even HDRI now. :)
Post a reply to this message
Attachments:
Download 'dodecf8ws.jpg' (149 KB)
Preview of image 'dodecf8ws.jpg'
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MUST... STEAL... FLOOR... CODE...
This excites me. I have been really interested in Penrose tiling for a while
now. So, the code for the floor really floored me. So, thank you genius!
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"Janet" <par### [at] attnet> wrote:
> MUST... STEAL... FLOOR... CODE...
Be my guest, Janet!
> This excites me. I have been really interested in Penrose tiling for a while
> now. So, the code for the floor really floored me. So, thank you genius!
Thanks, though I must also thank John VanSickle for the Penrose code in his
'Boxer' anim (an IRTC entry), which I originally based my code on.
Once you understand the Penrose code in this thread, you may want to take a
look at the code I posted last November, which uses two Penrose tilings
simultaneously: triangles and pentagons. The code is at
<web.4386daf17ed7ae6c2eef1b3b0@news.povray.org> and an image is at
http://news.povray.org/povray.binaries.images/attachment/%3Cweb.4386eb2d7ed7ae6c2eef1b3b0%40news.povray.org%3E/penroset
s.jpg?ttop=228370&toff=400
A top down view of just the floor is attached below.
That code uses a few 'interesting' techniques. If you need help
understanding anything in it, just ask.
Post a reply to this message
Attachments:
Download 'penroses2.jpg' (83 KB)
Preview of image 'penroses2.jpg'
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Wow, thanks so much Mr. Ring, actually if I ever understand it, it may be a
miracle, but I'll do my best. The one with the triangles and pentagons
together looks great too.
Janet
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"Janet" <par### [at] attnet> wrote:
> Wow, thanks so much Mr. Ring,
No worries.
> actually if I ever understand it, it may be a miracle, but I'll do my best.
:) Well, at least you probably already understand the role of the matrix in
reflecting the triangle.
Play with the code. Make all the triangles different colours so you can see
whats going on. Do scenes with low recursion depth to see how the triangles
get subdivided. Draw diagrams on paper. Investigate the geometry of the two
golden isoceles triangles:
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi2DGeomTrig.html#pentagon
There's also material on Penrose tilings on that page.
> The one with the triangles and pentagons together looks great too.
Thanks. That one did require a bid of hard thinking to combine the two, but
I think my solution is elegant.
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"PM 2Ring" <nomail@nomail> wrote:
> Play with the code. Make all the triangles different colours so you can see
> whats going on. Do scenes with low recursion depth to see how the triangles
> get subdivided. Draw diagrams on paper. Investigate the geometry of the two
> golden isoceles triangles:
>
> http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi2DGeomTrig.html#pentagon
>
> There's also material on Penrose tilings on that page.
>
> > The one with the triangles and pentagons together looks great too.
>
> Thanks. That one did require a bid of hard thinking to combine the two, but
> I think my solution is elegant.
I did play. Messed with a bunch of the variables. Messed with the angles
too, not so hot when you change them. :) Thanks for the link. I was looking
at a bunch of Penrose stuff and Phi stuff a while back. Played around with
equiangular spirals too, see ==> http://www.deviantart.com/view/29573733/
Well, I still need to play with the "triangles and pentagons" one too.
Thanks again!!!
Post a reply to this message
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"Janet" <par### [at] attnet> wrote:
> "PM 2Ring" <nomail@nomail> wrote:
> > Play with the code. Make all the triangles different colours so you can see
> > whats going on. Do scenes with low recursion depth to see how the triangles
> >
> > Thanks. That one did require a bid of hard thinking to combine the two, but
> > I think my solution is elegant.
Um, that should say "a bit of hard thinking". :)
>
> I did play. Messed with a bunch of the variables. Messed with the angles
> too, not so hot when you change them. :)
I bet!
> Thanks for the link. I was looking
> at a bunch of Penrose stuff and Phi stuff a while back. Played around with
> equiangular spirals too,
I did an equiangular spiral for my introductory RSOCP post:
//Pickover shell
#macro Shell(N,A,B,C,K)
#local D=(11/3-A)/N; #local I=1;
//union{
merge{
#while(I<N)
#local T=I/N; #local R=B*exp(A*K);
sphere{
R*<1,0,C/B>,R rotate z*A*360
pigment{rgb<T, .6, 1-T*T>}
finish{reflection{0,1} phong .7}
}
#local I=I+1; #local A=A+D;
#end
rotate x*30 translate <1,5,-2.5>
}
#end
>see ==> http://www.deviantart.com/view/29573733/
Interesting, but I agree with one of the comments that it's slightly creepy.
Speaking of which, do you know about Alexander's Horned Sphere"? It's been
called the ugliest object in mathematics.
> Well, I still need to play with the "triangles and pentagons" one too.
> Thanks again!!!
No worries!
Post a reply to this message
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"PM 2Ring" <nomail@nomail> wrote:
> "Janet" <par### [at] attnet> wrote:
> > "PM 2Ring" <nomail@nomail> wrote:
> > > Play with the code. Make all the triangles different colours so you can see
> > > whats going on. Do scenes with low recursion depth to see how the triangles
> > >
> > > Thanks. That one did require a bid of hard thinking to combine the two, but
> > > I think my solution is elegant.
>
> Um, that should say "a bit of hard thinking". :)
It took me three and a half hours to realize you spelled "bit" wrong.
I'll bet you're not in sales.
> >
> > I did play. Messed with a bunch of the variables. Messed with the angles
> > too, not so hot when you change them. :)
>
> I bet!
giggle
>
> > Thanks for the link. I was looking
> > at a bunch of Penrose stuff and Phi stuff a while back. Played around with
> > equiangular spirals too,
>
> I did an equiangular spiral for my introductory RSOCP post:
>
> //Pickover shell
> #macro Shell(N,A,B,C,K)
> #local D=(11/3-A)/N; #local I=1;
> //union{
> merge{
> #while(I<N)
> #local T=I/N; #local R=B*exp(A*K);
> sphere{
> R*<1,0,C/B>,R rotate z*A*360
> pigment{rgb<T, .6, 1-T*T>}
> finish{reflection{0,1} phong .7}
> }
> #local I=I+1; #local A=A+D;
> #end
> rotate x*30 translate <1,5,-2.5>
> }
> #end
It took me 5 minutes to find out what RSOCP was (crap, I've broken another
rule). I even saw your image in my "quest". Its excellent. I like the
colour change a lot. Actually, you're my favourite poster, seriously!!
I feel like a fookin' dope compared to the geniuses that post in the POV
Newsgroups, but that's why its fascinating.
> >see ==> http://www.deviantart.com/view/29573733/
>
> Interesting, but I agree with one of the comments that it's slightly creepy.
> Speaking of which, do you know about Alexander's Horned Sphere"? It's been
> called the ugliest object in mathematics.
Ugly math object? I will look it up right now! Cheers!
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"Janet" <par### [at] attnet> wrote:
> "PM 2Ring" <nomail@nomail> wrote:
> > Um, that should say "a bit of hard thinking". :)
> It took me three and a half hours to realize you spelled "bit" wrong.
Sorry, I had a cold. :)
> I'll bet you're not in sales.
Actually, I am in sales, kind of. I work in a call centre, taking orders for
disposable contact lenses from optometrists & their staff, but I don't
really do any actual selling or marketing.
> It took me 5 minutes to find out what RSOCP was (crap, I've broken another
> rule).
Don't worry, it's more like a tradition than a rule... but if you want
respect around here, you've gotta do one. :)
> I even saw your image in my "quest". Its excellent. I like the
> colour change a lot.
Yes, I was very happy to stumble onto that colour combo. I like playing with
colour spaces, but the best software I have for this is all on my Amiga.
> Actually, you're my favourite poster, seriously!!
Thanks! Flattery *will* get you everywhere, young lady. :)
> I feel like a fookin' dope compared to the geniuses that post in the POV
> Newsgroups, but that's why its fascinating.
Hey, compared to most of the population, anyone who can handle maths & 3D
geometry well enough to use POV is a genius. :) Besides, there has to be
some payoff for being a maths nerd. :)
> > >see ==> http://www.deviantart.com/view/29573733/
> >
> > Interesting, but I agree with one of the comments that it's slightly creepy.
> > Speaking of which, do you know about Alexander's Horned Sphere"? It's been
> > called the ugliest object in mathematics.
> Ugly math object? I will look it up right now! Cheers!
I've got a few pics of Alexander's Horned Sphere (AHS) on the Amiga, done
using an old version of POV. I'll get around to updating the eventually. In
the mean time, here's a couple on the net:
http://www.win.tue.nl/~aeb/at/hornedsphere.jpg
http://cs.stmarys.ca/~dawson/alexander.jpg
and of course
http://mathworld.wolfram.com/AlexandersHornedSphere.html
Although the AHS is topologically equivalent to a sphere, it behaves a bit
like a torus. If you tie a ribbon around it, you can't slip the ribbon off
in a finite number of steps, due to the infinite interlocking.
Alexander's Horned Sphere was discovered in the early years of the 20th
century. Back then, the fractals that had been discovered were considered
abnormal and pathological, so I guess that's why the AHS was called ugly.
Of course, all that changed with the work of Mandelbrot, et al.
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"PM 2Ring" <nomail@nomail> wrote:
> Sorry, I had a cold. :)
Ha ha!!
> Don't worry, it's more like a tradition than a rule... but if you want
> respect around here, you've gotta do one. :)
I see, maybe I should do one, if I think of something good for it.
> Although the AHS is topologically equivalent to a sphere, it behaves a bit
> like a torus. If you tie a ribbon around it, you can't slip the ribbon off
> in a finite number of steps, due to the infinite interlocking.
Sounds frustrating. :)
> Alexander's Horned Sphere was discovered in the early years of the 20th
> century. Back then, the fractals that had been discovered were considered
> abnormal and pathological, so I guess that's why the AHS was called ugly.
> Of course, all that changed with the work of Mandelbrot, et al.
"abnormal and pathological" fractals - too funny. Thanks for the pictures.
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