Marcia Selsor on tue 20 mar 07
Clarification:
In a recent NY times article about quasi crystalline structures and
Islamic tiles..mention was made of Penrose tessalations where the
patterns DO NOT repeat.
That is all. Most of the pattens do repeat and required complex math
which was said to demonstrate that the East preceded the West in this
advanced mathematical application by some 500 years. Penrose
tesselations also require complex math.
Marcia Selsor
http://marciaselsor.com
On Mar 20, 2007, at 10:14 AM, stephani stephenson wrote:
> Lea
> i just referred back to your post and read where you
> were asking about how these patterns differ..i.e. they
> seem to repeat and you were asking why Marcia said
> they didn't.
> Marci will likely have something to add or say on this
> but i can tell you what i was told from the gentleman
> who worked at repeating so many of these incredibly
> complex patterns in his home .
>
> When he started, he too thought it was a matter of
> repetition of a group of closely fitted shapes, based
> on geometry...(and in some cases it is, though often
> the repetition is of a number of shapes,
> interrelated).
>
> Often at the center would be ,say, a star with a
> certain number of points...
> but as the pattern radiated outward and he began to
> work with many of the larger medallions, he found that
> things began to happen
> and that there are unpredictable and irregularly
> shaped tiles which must be inserted to keep the
> pattern moving... though these irregular tiles often
> occur at regular intervals!
>
> it is almost impossible to detect these irregulat
> tiles unless they are pointed out to you, because they
> are so imbedded in this constellation of tiles which
> pattern and move before your eyes!
> i am not a mathematician so i cannot give you a
> mathematical reason, but
> this seems to be the case!
> also this mural work is done with great
> precision..traditional zillij being fired glazed and
> cut after glazing so they could be fit very close
> together. in this case tiles were cut from a somewhat
> stiff though able to be cut..the tool is sharper and
> thinner than a fettling knife, actually a needle tool
> which has been sharpened on one edge then the sides of
> each tiny tile has it's edges gently smoothed....
>
> the grout space in between the finished tiles is about
> 1/32 inch, yet
> even with such precision, once you start radiating
> outward, the patterns take on additonal layers of
> interrelationship.....
> and they seem to move an turn on invisible axes
> (axises, axi?)
>
> that's why i got goose bumps hearing a few weeks ago
> that they resemble quasi crystalline structures.... it
> is really one of those wonderful metaphoric images,
> especially if you also think about them as attempt to
> express the divine in someone's faith, yet something
> which touches on geometry, geology, physics, botany,
> and of course, color pattern art and beauty, oh and
> function too.
>
stephani stephenson on tue 20 mar 07
Lea
i just referred back to your post and read where you
were asking about how these patterns differ..i.e. they
seem to repeat and you were asking why Marcia said
they didn't.
Marci will likely have something to add or say on this
but i can tell you what i was told from the gentleman
who worked at repeating so many of these incredibly
complex patterns in his home .
When he started, he too thought it was a matter of
repetition of a group of closely fitted shapes, based
on geometry...(and in some cases it is, though often
the repetition is of a number of shapes,
interrelated).
Often at the center would be ,say, a star with a
certain number of points...
but as the pattern radiated outward and he began to
work with many of the larger medallions, he found that
things began to happen
and that there are unpredictable and irregularly
shaped tiles which must be inserted to keep the
pattern moving... though these irregular tiles often
occur at regular intervals!
it is almost impossible to detect these irregulat
tiles unless they are pointed out to you, because they
are so imbedded in this constellation of tiles which
pattern and move before your eyes!
i am not a mathematician so i cannot give you a
mathematical reason, but
this seems to be the case!
also this mural work is done with great
precision..traditional zillij being fired glazed and
cut after glazing so they could be fit very close
together. in this case tiles were cut from a somewhat
stiff though able to be cut..the tool is sharper and
thinner than a fettling knife, actually a needle tool
which has been sharpened on one edge then the sides of
each tiny tile has it's edges gently smoothed....
the grout space in between the finished tiles is about
1/32 inch, yet
even with such precision, once you start radiating
outward, the patterns take on additonal layers of
interrelationship.....
and they seem to move an turn on invisible axes
(axises, axi?)
that's why i got goose bumps hearing a few weeks ago
that they resemble quasi crystalline structures.... it
is really one of those wonderful metaphoric images,
especially if you also think about them as attempt to
express the divine in someone's faith, yet something
which touches on geometry, geology, physics, botany,
and of course, color pattern art and beauty, oh and
function too.
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Marcia Selsor on wed 21 mar 07
Steve,
That is really an interesting site. I have always been interested in
patterns and geometry.
I had an old program called Escher-sketch, or something like that/ It
became obsolete
when I upgraded my operating system. Maybe there is an upgrade out
there.
Some of the tessellations were developed like the islamic ones using
grids and arcs.
I'd like to know what that contraption was on one of the links that
looked like "draw a
straight line but it turns into a curve. Thanks for posting that site.
>
> It's all at http://www.cromp.com/tess/home.html .
>
> Steve S.
>
Marcia Selsor
http://marciaselsor.com
Lea Holland on wed 21 mar 07
Marcia,
The standard graphic design "drawing" program, Adobe Illustrator, would be
ideal for this project. It allows you to duplicate the tiles quickly, rotate
individual or groups of shapes, automatically "stick" to a point or line,
etc. You can draw straight lines that turn into curves, and specify the
angle of the curve mathematically, etc. The learning curve is steeper than
an Etch-it-Sketch, but it's powerful!
You can download free "try it" versions at:
http://www.adobe.com/downloads/#product=27
Lea
>I had an old program called Escher-sketch, or something like that/ It
>became obsolete
>when I upgraded my operating system. Maybe there is an upgrade out
>there.
>Some of the tessellations were developed like the islamic ones using
>grids and arcs.
>I'd like to know what that contraption was on one of the links that
>looked like "draw a
>straight line but it turns into a curve. Thanks for posting that site.
>>
>> It's all at http://www.cromp.com/tess/home.html .
>>
>> Steve S.
>>
Lea Holland on wed 21 mar 07
>Lea
>i just referred back to your post and read where you
>were asking about how these patterns differ..i.e. they
>seem to repeat and you were asking why Marcia said
>they didn't.
***Stephani,
I'm glad Marcia clarified her statement, but let me clarify mine too: the
writer of the NYT article, and Professor Lu said the Penrose patterns don't
repeat, I didn't say that Marcia said that...it's so confusing...
> Often at the center would be ,say, a star with a
>certain number of points...
>but as the pattern radiated outward and he began to
>work with many of the larger medallions, he found that
>things began to happen
>and that there are unpredictable and irregularly
>shaped tiles which must be inserted to keep the
>pattern moving... though these irregular tiles often
>occur at regular intervals!
***That's almost exactly what the physicists said: predictable, unrepeating.
There are also some rules about rotating in Islamic tradition that were
beyond me (see Lu article).
>
>it is almost impossible to detect these irregulat
>tiles unless they are pointed out to you, because they
>are so imbedded in this constellation of tiles which
>pattern and move before your eyes!
>i am not a mathematician so i cannot give you a
>mathematical reason, but
>this seems to be the case!
>also this mural work is done with great
>precision..traditional zillij being fired glazed and
>cut after glazing so they could be fit very close
>together. in this case tiles were cut from a somewhat
>stiff though able to be cut..the tool is sharper and
>thinner than a fettling knife, actually a needle tool
>which has been sharpened on one edge then the sides of
>each tiny tile has it's edges gently smoothed....
>
>the grout space in between the finished tiles is about
>1/32 inch, yet
>even with such precision, once you start radiating
>outward, the patterns take on additonal layers of
>interrelationship.....
>and they seem to move an turn on invisible axes
>(axises, axi?)
*** I had to look it up too. It's axes.
> that's why i got goose bumps hearing a few weeks ago
>that they resemble quasi crystalline structures.... it
>is really one of those wonderful metaphoric images,
>especially if you also think about them as attempt to
>express the divine in someone's faith, yet something
>which touches on geometry, geology, physics, botany,
>and of course, color pattern art and beauty, oh and
>function too.
*** Well said. I couldn't agree more.
stephani stephenson on wed 21 mar 07
Lea , Steve ,marcia and all
thanks for clearing up the misread Lea! Steve your
grotesque geometry is cool!
lets see, just to follow ,looselt , the thread of
conversation...
the 'regular irregulars' in the large panels are
fascinating to me, as are the occasional "irregular
irregulars", which may perhaps happen, who knows, when
real man made tiles begin to execute the dance of
mathematics, in sometimes dizzying complexity....for
our pattern seeking eyes and minds
a couple of other things which struck me , as i
mentioned in the slide presentation...
that , in the complex patterns, because of the close
fitting nature, certain tiles had to be "dropped in"
after the panels were laid out to 'lock' the smaller
panels together, as the shape could not be
successfully fit in beforehand
and also
the person who did this was very well versed in
computer composition
of these patterns. Even so, i gathered that there was
a fair amount of computer work involved, enough that
he was
in awe of how these things were originally conceived,
determined,composed, fabricated ,and installed.
the ENJOYMENT part of course, as Steve and you and
Marci have alluded to ...
is strangely and universally easy !!!!!!
i dont' know too many in this country who work with
zillij, though the art is still practiced in
locations, in Northern Africa for example. This
really is mosaic work of an intensley ordered and
precise nature.
the people i know here who work with tessellated tile
often employ false grout lines and make tiles composed
of more than one unit at a time which lessens somewhat
the time involved and also improves the
success of fit... also the ones here use grout, and
offten to an attractive use, setting off the tile
color, whereas the original zillij technique does not
use grout, the tiles are fit right up against each
other.
also i must note...i don't do this type of work myself
and and know it
from reading, viewing and interviewing only, not from
the inside out!!!!! so my knowledge on these aspects
is limited.
years ago i carved some pots, covering them with
tessellations derived from Escher patterns, which i
thoroughly enjoyed, especially fitting the pattern to
rounded and irregular vessel forms..... i still love
the intricacy of tesellated tile, but
find my own inclination to work differently
There's a lot of knowledge and discovery on this
list. amazing what is out there in the world.
Stephani
http://www.revivaltileworks.com
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claystevslat on wed 21 mar 07
Marcia -- Was the program Escher Web Sketch? It's been rewritten
in Java so those of us who are Mac-deprived can get it too. There
are current (and, presumably, currently working) versions for download
at http://escher.epfl.ch/escher/ .
Steve S
--- In clayart@yahoogroups.com, Marcia Selsor wrote:
>
> Steve,
> That is really an interesting site. I have always been interested in
> patterns and geometry.
> I had an old program called Escher-sketch, or something like that/ It
> became obsolete
> when I upgraded my operating system. Maybe there is an upgrade out
> there.
claystevslat on wed 21 mar 07
Hi --
Just poking a comment in here for those who may
be interested in the tessellation thing -- there
is lots of interesting math behind this, but you
don't need to know a bit of it to appreciate it
-- this is one of these cases where the result of
the mathematical principle is evident even if the
principle is unknown (like the calculus you'd have
to work out to figure out where exactly a thrown
tennis ball would fall to the earth -- a result
that is evident not only to a tennis player who
knows no math, but to any reasonably well-trained
dog).
If you want to see some background on the tessellations
that DOESN'T REQUIRE UNDERSTANDING THE MATH, you
can go to the GROTESQUE GEOMETRY page maintained by
Andrew Crompton, which has lots of fractal images,
tessellations, examples of repeated interlocked
images, etc.
It's all at http://www.cromp.com/tess/home.html .
Steve S.
--- In clayart@yahoogroups.com, stephani stephenson
wrote:
>
> Lea
> i just referred back to your post and read where you
> were asking about how these patterns differ..i.e. they
> seem to repeat and you were asking why Marcia said
> they didn't.
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