The complex geometry of Islamic design - Eric Broug

伊斯蘭的幾何拼貼 - Eric Broug

譯者: 東慶 陳 審譯者: 安強 朱

In Islamic culture, geometry is everywhere.

在伊斯蘭文化中, 幾何隨處可見

You can find it in mosques, madrasas, palaces and private homes.

在清真寺,學校,宮殿,跟私人住宅中 都看的到幾何拼貼

This tradition began in the 8th century CE during the early history of Islam,

這傳統始於8世紀,伊斯蘭文化的初期

when craftsmen took preexisting motifs from Roman and Persian cultures

那些工匠在先前的 羅馬與波斯文化中取得靈感

and developed them into new forms of visual expression.

並發展出新形式的視覺表現

This period of history was a golden age of Islamic culture,

這段時期是伊斯蘭的黃金時期

during which many achievements of previous civilizations

在這段時間,許多先前的文化成就

were preserved and further developed,

得以保存並發展

resulting in fundamental advancements in scientific study and mathematics.

致使科學與數學能有所推展

Accompanying this was an increasingly sophisticated use of abstraction

隨之而來的是,越來越抽象

and complex geometry in Islamic art,

與複雜的幾何圖形 被使用在伊斯蘭藝術中

from intricate floral motifs adorning carpets and textiles,

從複雜的花紋地毯與紡織品

to patterns of tilework that seemed to repeat infinitely,

到鋪磚的拼貼圖案 都有到無止盡的重複排列

inspiring wonder and contemplation of eternal order.

引發我們的驚奇並思考那永恆的規律

Despite the remarkable complexity of these designs,

儘管這些設計相當複雜

they can be created with just a compass to draw circles

仍可僅靠圓規與

and a ruler to make lines within them.

直尺來繪製

And from these simple tools emerges a kaleidoscope multiplicity of patterns.

從這些簡單的工具 創造有如萬花筒一般多樣的圖案

So how does that work?

那要如何繪製呢？

Well, everything starts with a circle.

一切都始於一個圓

The first major decision is how will you divide it up?

首先要決定的是我們要把它分成幾份

Most patterns split the circle into four, five or six equal sections.

大部份的樣式是將圓分成 4, 5 或 6 份

And each division gives rise to distinctive patterns.

然後給予每個部份一個特別的圖案

There's an easy way to determine whether any pattern is based on fourfold,

有一個簡單的方法可以判別它是 4 對稱,

fivefold,

5 對稱,

or sixfold symmetry.

或 6 對稱

Most contain stars surrounded by petal shapes.

一般而言會有一個星型被其他形狀所環繞

Counting the number of rays on a starburst,

可以數星型的角

or the number of petals around it,

或周圍形狀的數量

tells us what category the pattern falls into.

便可知道它是幾個對稱

A star with six rays, or surrounded by six petals,

一個有 6 個角的星形 或者它周圍有 6 個形狀

belongs in the sixfold category.

它便屬於 6 對稱

One with eight petals is part of the fourfold category, and so on.

而有 8 個角的屬於 4 對稱,依此類推

There's another secret ingredient in these designs:

在這設計中還有另外一個特性

an underlying grid.

「基本網格」

Invisible, but essential to every pattern,

雖然無法直接看到 但每個圖形皆有它的身影

the grid helps determine the scale of the composition before work begins,

在開始作圖之前 這網格能確定圖形的規模

keeps the pattern accurate,

保持圖案的精確度

and facilitates the invention of incredible new patterns.

並且有利於創造美妙的新圖案

Let's look at an example of how these elements come together.

我們來看個例子來了解 這些作圖元素結合在一起

We'll start with a circle within a square, and divide it into eight equal parts.

先畫一個圓並且用正方形包住它 接著再把圓八等分

We can then draw a pair of criss-crossing lines

我們可以任選等分點來畫出一對線條

and overlay them with another two.

並且用另外的兩個來覆蓋它們

These lines are called construction lines,

這些線叫做「作圖線」

and by choosing a set of their segments,

藉由選擇一組線段

we'll form the basis of our repeating pattern.

我們可以以這些線當基礎 來畫重複的圖案

Many different designs are possible from the same construction lines

許多不同的設計都可以 由同一作圖線所創造

just by picking different segments.

只是選擇不同組的線段

And the full pattern finally emerges

而最終完整的圖便出現了

when we create a grid with many repetitions of this one tile

當我們用重複的基本網格 來創造一個格狀拼貼

in a process called tessellation.

這一個過程稱作「鑲嵌」

By choosing a different set of construction lines,

藉由選擇不同組的作圖線

we might have created this pattern,

我們可能已經完成這個圖案

or this one.

或這個圖案

The possibilities are virtually endless.

這些圖案是無止盡的

We can follow the same steps to create sixfold patterns

我們可以藉由一樣的方法 來畫出6個對稱圖案

by drawing construction lines over a circle divided into six parts,

藉由畫出作圖線並包覆等分圓的6個部份

and then tessellating it, we can make something like this.

並且鑲嵌它,我們便可做出這個圖案

Here's another sixfold pattern that has appeared across the centuries

這是另一個6對稱的圖案,已經有百年歷史

and all over the Islamic world,

並且遍及整個伊斯蘭

including Marrakesh, Agra, Konya and the Alhambra.

包括馬拉喀什,阿格拉,科尼亞 和阿罕布拉

Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid.

4對稱適用在方格網 而6對稱適用於6邊形網

Fivefold patterns, however, are more challenging to tessellate

可是,5對稱的鑲嵌極具挑戰性

because pentagons don't neatly fill a surface,

因為5邊形無法整齊的填滿表面

so instead of just creating a pattern in a pentagon,

因此,不僅僅使用五邊形的圖案

other shapes have to be added to make something that is repeatable,

還會加入其他的形狀使得圖案得以重複

resulting in patterns that may seem confoundingly complex,

導致圖案極為複雜

but are still relatively simple to create.

但其依然易於製造

Also, tessellation is not constrained to simple geometric shapes,

鑲嵌並未限制於簡單的幾何圖形

as M.C. Escher's work demonstrates.

就如同艾雪的作品所展示的

And while the Islamic geometric design tradition

儘管伊斯蘭傳統的幾何設計

doesn't tend to employ elements like fish and faces,

並無採用像魚跟人臉的元素

it does sometimes make use of multiple shapes to craft complex patterns.

但有時使用多重的圖形來製造複雜的圖案

This more than 1,000-year-old tradition has wielded basic geometry

這 1000 年以上的歷史傳統利用基礎幾何

to produce works that are intricate, decorative and pleasing to the eye.

來製造錯綜複雜又好看的裝飾品

And these craftsmen prove just how much is possible

而這些工匠透過 藝術直覺,創意,奉獻精神

with some artistic intuition, creativity, dedication and a great compass and ruler.

以及一把好的圓規與直尺 來實現這些可能性