a work in progress.......
Quadhall

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Quadhall wrote:
> 
> a work in progress.......

A pedantic nitpick, but while the red and blue tiles are shaped like
those of a Penrose tiling, they are not arranged in the Penrose pattern.

Regards,
John
-- 
ICQ: 46085459

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John VanSickle wrote:
> A pedantic nitpick, but while the red and blue tiles are shaped like
> those of a Penrose tiling, they are not arranged in the Penrose pattern.

Tangentially I wonder whether it's possible to cover a sphere with tiles
topologically equivalent to Penrose's.

-- 
Anton Sherwood  --  br0### [at] p0b0xcom  --  http://ogre.nu

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Anton Sherwood wrote:
> 
[...]
> Tangentially I wonder whether it's possible to cover a sphere with tiles
> topologically equivalent to Penrose's.
> 

I'm no expert in spherical geometry, but that could be possible if you would
distort the single tiles a bit (change angles).  The structure of real penrose
tiling is quite irregular, so this could be quite difficult... you will probably
have to work with variable distortion.

I could think of a program where the tiling grows and angles are adaptively
modified to follow a sphere's shape.  I'm not sure if that works, probably
things would not fit together in the end.  

Christoph

--
Christoph Hormann <chr### [at] gmxde>
Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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I'm sure there must be a way to cover a sphere, but your pattern

too. But You surely know that you can aproximate a sphere by n
equal-sided triangles, where n are some discrete numbers...

I don't know if it will work, to take 2 of these triangles
together, but maybe you can get your' penrose tiling this way to
the sphere ...

hmm ... quite hard to explain, hope you know what I mean...

--

 ,',    Jan Walzer      \V/  http://wa.lzer.net     ,',
',','   student of      >|<  mailto:jan### [at] lzernet ',','
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Thanks for pointing that out--->I won't change this image as a result, but
perhaps I will incorportate a true Penrose tiling in a future image.  Oh,
and nitpick away, it helps me to learn and stay humble (not that I have much
reason not to be humble).  Thanks again.


John VanSickle wrote in message <39725C85.4B510B8E@erols.com>...
>Quadhall wrote:
>>
>> a work in progress.......
>
>A pedantic nitpick, but while the red and blue tiles are shaped like
>those of a Penrose tiling, they are not arranged in the Penrose pattern.
>
>Regards,
>John
>--
>ICQ: 46085459

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On Sun, 16 Jul 2000 21:08:21 -0400, John VanSickle wrote...
> Quadhall wrote:
> > 
> > a work in progress.......
> 
> A pedantic nitpick, but while the red and blue tiles are shaped like
> those of a Penrose tiling, they are not arranged in the Penrose pattern.

I thought that the whole point of penrose tiling was that there *was* no 
pattern, that you could fling the tiles together almost randomly and 
still get them to tesselate...

I could easily be wrong though.

Bye for now,
     Jamie.

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Jamie Davison wrote:
> 
[...]
> 
> I thought that the whole point of penrose tiling was that there *was* no
> pattern, that you could fling the tiles together almost randomly and
> still get them to tesselate...
> 
> I could easily be wrong though.
> 
> Bye for now,
>      Jamie.

IIRC, penrose tilings have a nonperiodic structure, but they are based on very
simple rules, for example fractint describes penrose tiling with the following
L-System:

Penrose1 {
  Angle 10
  Axiom +WF--XF---YF--ZF
  W=YF++ZF----XF[-YF----WF]++
  X=+YF--ZF[---WF--XF]+
  Y=-WF++XF[+++YF++ZF]-
  Z=--YF++++WF[+ZF++++XF]--XF
  F=
}

So there is only one unique penrose tiling, and changing any element, even if
the tiling stays complete, would no more be a real penrose :-)

Christoph

--
Christoph Hormann <chr### [at] gmxde>
Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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Jamie Davison wrote:
> I thought that the whole point of penrose tiling was that there *was* no
> pattern, that you could fling the tiles together almost randomly and
> still get them to tesselate...

It's not periodic, but (iirc) every infinite Penrose tiling contains
every finite Penrose tiling -- *because* it is not periodic.

-- 
Anton Sherwood  --  br0### [at] p0b0xcom  --  http://ogre.nu/

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John VanSickle wrote:
> 
> Quadhall wrote:
> >
> > a work in progress.......
> 
> A pedantic nitpick, but while the red and blue tiles are shaped like
> those of a Penrose tiling, they are not arranged in the Penrose pattern.
> 
	Well, according to this page:
http://mathworld.wolfram.com/PenroseTiles.html they're not
even shaped like a Penrose tiling's tiles...

		Jerome
-- 

* Doctor Jekyll had something * mailto:ber### [at] inamecom
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