In message <web.42dcff7c811cc7c3d46eca60@news.povray.org>, PM 2Ring 
<nomail@nomail.?.invalid> writes
>Alex <pov### [at] lazysodorguk> wrote:
>> In message <web.42d322fa811cc7c3ad93754b0@news.povray.org>, PM 2Ring
>> <nomail@nomail.?.invalid> writes
>> >Alex <pov### [at] lazysodorguk> wrote:
>>
>> >> Currently unemployed, I decided to have another crack at doing Penrose
>> >> tiles, the hard way. After a week I gave up and did them the easy way :)
>
>What's the hard way? Placing them "by hand". I've done a few like that...
>
Projecting a specific subset of a 5 dimensional integer lattice onto a 2 
dimensional plane to give the vertices of the rhombs. The principle is 
very simple, and it's easy to do with a 3 dimensional lattice, but for 
the life of me I can't work out the nitty gritty of the higher 
dimensional cases. All the resources I can find just explain the 
principle.

Method discovered by deBruijn.

See http://gregegan.customer.netspace.net.au/APPLETS/12/12.html for an 
example, click the applet until you get Penrose tiling. Some of the 
other applets on the site are well worth checking out, "Wythoff" is 
another stunning one which gave my a couple of ideas for geomag.

>> >They can be tricky! :) What technique did you use? Here's one I posted back
>> >in April:  <web.425b6e5da45a985aad93754b0@news.povray.org>
>> >
>> See other post. I'm afraid I must have missed your post, I've been
>> subscribed to the group for some time but skipped some posts recently in
>> order to catch up. I shall attempt to request it with my newsreader!
>
>And I missed this post (and the one from Thomas), but I just use the Web
>interface. If you want to see my earlier pic, the Web interface may be the
>easiest way, because from here, links like the one above are live.
>
>> >I first started using Penrose macros from Boxer by John VanSickle, but I
>> >ended up making up my own macros. I can post the sources if anyone's
>> >interested.
>> >
>> I remember seeing some of those animations. Some interesting patterns &
>> objects. Can't say I can remember any Penrose tiles, I may go look
>> later.
>
>I never actually saw the Boxer animations. I found it through Google,
>searching for "Penrose tiling". From the source code, the Boxer anim uses a
>simple flat Penrose tiling for the floor.
>
Just found it on my HDD. The tiling was quite subtle, I never noticed it 
before!

>> >FWIW, you can get very
>> >powerful magnets out of dead hard drives.
>> >
>> I've taken 2 apart before. I have several other dead ones I could
>> dismantle. The magnets are very brittle, though.
>
>Very brittle, indeed. And they can attract each other with enough force to
>fracture them, so I have lots of small pieces of them. These magnets are
>*not* toys! Keep out of reach of children! Skin pinched between
>supermagnets is painful! :)

Glad I'm not the only stupid person :)

>
>> >Anyway, here's a close-up of an earlier Penrose tiling I did. We seem to
>> >have chosen similar colour schemes.
>> >
>> I chose my colours so they averaged to 50% grey, that was the first pair
>> I found that didn't look awful.
>
>:) Things start getting awfully muddy down at that greylevel.
>
I lied about my colour scheme, all the pairs of colours looked awful so 
I used something different.

>>I thought it might help the appearance
>> of the blurred reflections of distant tiles.
>
>That makes sense. Still, the floor is a little too dark for my tastes.

Maybe. But make everything bright and the highlights don't show up as 
much. It's a difficult one to judge.

>
>> And you've done proper
>> curved edges, I just did a flat bevel by intersection of planes.
>
>Those curved edges... They were a bit trickier than I thought they were
>going to be. I ended up making one macro for rounded isoceles triangle
>tiles, and another one for rounded polygonal prisms. I suppose I should
>tidy them up a bit and post them.
>
That's why I didn't bother. Achieving a constant width gap between 
different shaped tiles was tricky enough.

>Here's a Penrose tiling, using rounded pentagonal prisms, in standard stone
>textures. The tiles were placed by simple #while loops, not recursive
>macros.
>
Similar to a "pentaflake" fractal, but with some pentagons filling the 
larger gaps.
-- 
Alex

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