Islamic Penrose Tiles - for Sam

S

sowhatifit'sdark

Valued Senior Member
I thought this was rather interesting

Islamic architects and mathematicians were creating quasi-crystalline patterns some 500 years before similar patterns were described in the West, claim two physicists in the US. Peter J Lu of Harvard University and Paul Steinhardt of Princeton University say that sets of special tiles developed around the 13th century allowed artisans to use complex mathematics to create the fantastic geometric patterns that adorn mosques, palaces and other buildings in the Muslim world. These patterns include "nearly perfect" Penrose patterns, which the researchers claim are similar to the first quasicrystals described in 1974 by the British mathematical physicist Roger Penrose (Science 315 1106).
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http://www.sciencenews.org/articles/20070224/mathtrek.asp
 
thank you Iran

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I wonder at the artisans who had to join these tiles to create that perfect symmetry.

Could such dedication be found today?

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sowhatifit'sdark: Thanks :)
 
My math is far too weak to fully appreciate the patterns except aesthetically, which I do, but I found the properties of these tiles very interesting.

Remarkable Properties of Penrose Tilings
The most remarkable property of Penrose Tilings is that every finite portion of any tiling is contained infinitely often in every other tiling. This, of course, is true of all periodic tilings, but it's not at all obvious that it should be true of a non-periodic tiling. This property has several consequences:

No finite patch of tiles can force a tiling (determine the rest of the tiling).
It is impossible to tell from any patch of tile which tiling it is on.
Only at their infinite limits are the different patterns distinguishable. A finite patch of an Infinite Star pattern might only be a local piece of some other pattern, but there is also an Infinite Star pattern that has five-fold symmetry to infinity. Only if you know the characteristics of the pattern to infinity can you tell.
This property is both less and more remarkable than it seems. For example, consider the numbers pi (3.14159265358979326433....), e (2.718281828459045235360287...) and the square root of 2 (1.4142135623730950488...). All of them contain the number sequences ..23.. and ..35.. . In fact, it is widely believed (though not formally proven) that any finite sequence of digits will be contained infinitely often in all three numbers, and no finite sequence of digits will enable you to tell which number you are looking at (except, of course, for the integer and decimal point).

What's remarkable about the Penrose Tilings is how dense the patterns are. The sequence ...89793... occurs infinitely often in pi, e, and the square root of 2, but only every 100,000 digits on the average, and the actual spacing could be vastly greater. In fact, there is no known upper limit. If a patch of tiles in a Penrose tiling has a diameter d, there will be an identical patch within a distance of at most 2d and most likely within d. (See how close to the center of the cartwheel above you can find another Batman.)
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http://www.uwgb.edu/DutchS/symmetry/penrose.htm
 
Control System engineering with aerospace sector are way more complicated and devoted to one systematic goal...by ways of matrix linear algebra calculations embedded within control system designs.

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At first glance, they appear to be the work of masterful artists. However, they were only forced to make patterns like these because depiction of the human form is forbidden. Every time I see these examples, I can only think of how it must be, as an artist, to live in such a totalitarian state.
 
spidergoat said:
At first glance, they appear to be the work of masterful artists. However, they were only forced to make patterns like these because depiction of the human form is forbidden. Every time I see these examples, I can only think of how it must be, as an artist, to live in such a totalitarian state.
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In some articles on these tiles I see 500 years ago, in others 800. Shall we peek over in Europe and see what some of the totalitarian states were doing there and how free artists were?

Or what started, about 500 years ago, in the New World?

Come on. Oddly enough, there are people today in the west who make abstract patterns in tile.

In a general way I do agree with you. I dislike how nearly all cultures have limited humans and artists unnecessarily, but in this context yours seemed an odd contribution.
 
sowhatifit'sdark said:
Shall we peek over in Europe and see what some of the totalitarian states were doing there and how free artists were?
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Quentin Massys
Ill-Matched Lovers, c. 1520/1525
 
spidergoat said:
At first glance, they appear to be the work of masterful artists. However, they were only forced to make patterns like these because depiction of the human form is forbidden. Every time I see these examples, I can only think of how it must be, as an artist, to live in such a totalitarian state.
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So there is example of Penrose tiling from the Western artists of the time?

Mughal miniature art :

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Islamic metalwork

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More Penrose tiling in arabesque:

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More Islamic metalwork:

The axe has calligraphy on it spelling out the name Ali (علي) forwards and backwards

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OK, perhaps I was exaggerating about the lack of human forms, but they certainly seem rather 2-dimensional.
 
spidergoat said:
OK, perhaps I was exaggerating about the lack of human forms, but they certainly seem rather 2-dimensional.
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I think they were into more detail work than brushstrokes. Much of Islamic art is highly characterised by attention to minutae.

Like calligraphy:

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Or marble latticework:

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And the tiling.
 
More calligraphy in Penrose in a niche (mihrab) of a mosque:

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Its interesting how they must have worked out the precision to the nth decimal.
 
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