Moroccan Mosaics: A Creative Blend of Art, Nature, and Mathematics

New York – Mathematicians and scientists can spend a lifetime’s work identifying and evaluating patterns. The golden ratio is a set of numbers that occur in nature in a specific pattern.

The ratio, also known as the Fibonacci sequence, dictates the arrangement of branches in a tree and the number of petals on a flower. The golden ratio is an overt reminder of the ways that math plays into everyday life, and of its effortless beauty.

I thought about the beauty of mathematics as I stood in the courtyard at the University of al- Qarawiyyin, the oldest university in the world, in the Fez medina. I was looking at a walled pattern designed with hundreds of small stones, entranced by its beauty and fascinated by its perplexing mathematical structure.

The brilliant colors invoked feelings that I could neither explain nor comprehend. It was just a pattern, but for a moment the world receded and I was alone with the marvelous imagery.

I escaped my trance and decided I must know more about the ancient Islamic tiling. I wanted to know how it was created, what disciplines contributed to its creation, and what fantastic mathematics hid behind its beauty.

I discovered that I was looking at “zellige,” meaning little polished stone in Arabic. Tiles lined the courtyard’s walls, floor, and central fountain. Zellige is an amazing feat of the Islamic world, dating back to the 8th century. The University of al-Qarawiyyin was built in 859, so I was looking at some of the art’s earliest examples.

The art of zellige has its own history

The tiling art began with simple shapes and patterns influenced by Greek and Roman mosaics. As time went on, the patterns became more and more complex. By the 17th century, intricate designs included stars with up to 16 points.

Creating zellige involves the combined talents of artists, artisans, and mathematicians. It represents the incredible innovation of the ancient Islamic world. The mosaics are drawn with ruler and compass and are generated with simple underlying patterns made from circles and squares. These are combined, duplicated, overlaid, and expanded upon to create the final product.

The resulting patterns are tessellations, a repetition that creates an illusion: The image seems to extend beyond the boundaries of the wall it was laid upon, invoking a sense of infinity. The grandness of the seemingly infinite art had its desired effect on me. I was humbled.

Zellige may have evolved due to aniconism, or the prohibition of imagery of sentient beings that is found in much of Islam. The mosaics were a method for people to portray religious stories and values that they could not depict through realism. The mosaics are intended to invoke feelings of faith and passion in the viewer, similar to how religious scenes may act in another culture. Each shape and color has a purpose.

A marriage of art and math

Zellige also represents the ancient Islamic world’s mathematical capabilities and advancements. I was not the only one fascinated by the combined beauty and complexity of zellige. Many have questioned how the two play together, and what makes the art so captivating. There is even a realm of mathematics dedicated to patterns and mosaics, a subject zellige falls neatly into.

Metin Arik, a mathematician who studies this category, has a theory about zellige and its surprising relation to a “freak of nature.” Although it is contested, Arik suggests that the mosaics have a striking similarity to a unique crystal known as a quasicrystal.

Shining a light through the crystal, a pattern will emerge from the beam. This diffraction pattern is one way scientists determine the crystal’s structure. A quasicrystal is unique: It shares many properties of normal crystals, but lacks some fundamental properties.

A typical crystal has a predictable structure with three-, four-, or six-fold symmetry. A quasicrystal can present five-fold symmetry. Five-fold symmetry is unique because it does not have translational symmetry: One portion of a pattern is not identical to other portions. This deviates from one of the fundamental properties of a crystal, making the quasicrystal a “freak of nature.”

A quasicrystal’s diffraction pattern has an uncanny resemblance to zellige, with similar arrangements and similar properties, including symmetry. Arik states that by the 15th century, zellige designs had become so complex that they constructed “nearly perfect quasi-crystalline … patterns, five centuries before their discovery in the West.” Arik marvels at the incidental similarity of zellige to one of nature’s most bizarre phenomena.

The artistry continues to mystify me

The creation and existence of zellige is far more complex than I had anticipated when I entered the university courtyard. The blend of art and math revealed far more paths of exploration than I could have imagined. Zellige is still researched today, and mathematicians far and wide are continuously surprised by their discoveries.

Zellige can be found all over Morocco, from private homes to water fountains accessed by entire neighborhoods. I still marvel at its complexity, its beauty, and its abundance. I came nowhere near to addressing all of the questions that apply to zellige, but I am satisfied with what I discovered.