Re: Penrose Tilings

HI Kraig,

Sounds like a nice idea to use the Penrose tilings in a garden.
The crystals have gaps too, and as you change the way in which
they form, there's an optimal postion at which the "tiles" of
the crystal fit together perfectly without gaps (as far as
one can tell), as I remember reading when I was researching into non
periodic tilings.

Also the study of Penrose tilings with gaps is an interessting
area - for instance, if you have a large tiling that tiles
to infinity, but has a gap in it, what kinds of gap are
possible there, that sort of thing. It relates to the crystals
work because the crystals have gaps.

Also, maybe they have foudn out more now, but when I was working
on the maths and reading the crystallography journals to see
what they said about it all, it was somethign of a puzzle to
know how the crystals could manage to tile a near perfect
penrose tiling (or various generalisations of the Penrose
tiling) because of the property that you sometimes need to know the
position of a tile arbitrarily far away in the tiling before you know
where to position the next tile in the tiling - otherwise you
can get so far and then find you can get no further. So
how do the crystals manage it given that usually one thinks
of them as growing in a local fashion. Roger Penrose wondered
if possibly there might be some long range quantum effect
involved.

However that is a few years ago and I haven't kept up with it
all and am probably out of date now.

Robert

> Sounds like a nice idea to use the Penrose tilings in a garden.

...and Sierpinski carpets in the living room!

Dante

--- In tuning@y..., "Dante Rosati" <dante.interport@r...> wrote:
> > Sounds like a nice idea to use the Penrose tilings in a garden.
>
> ...and Sierpinski carpets in the living room!
>
> Dante

And if you spill some Cantor dust on it you can clean it up with a Menger sponge.

Oy! Too much silly.
John Starrett