Muqarnas are intricate, ornamental vaultings found in Islamic and Persian architecture. They are complex stalactite-like structures that combine elements of architecture, mathematics, and art, recognized for their beauty throughout history.

Where can Muqarnas typically be found?

Historically, muqarnas are a prominent feature in Islamic and Persian architecture. They are often used in domes, portals, iwans, and cornices of mosques, palaces, and tombs, creating stunning three-dimensional geometric patterns.

What is unique about the traditional design of Muqarnas?

Traditional muqarnas are considered early and impressive examples of rule-based architectural design. They are abstract, non-figurative formations built upon underlying geometric principles, leading to their highly intricate and complex appearance.

How is Michael Hansmeyer's project reinterpreting Muqarnas?

Michael Hansmeyer's project reinvents traditional muqarnas using computational design and robotic fabrication. It explores how modern technology can extend this rule-based geometric art into the future, creating new and unseen formations.

What role does computation play in generating these modern Muqarnas?

In this project, the computer acts as a tool for search and exploration, enabling the generation of endless permutations of designs. It employs a selective subdivision algorithm to create intricate ceiling plans, resulting in novel forms with millions of tiles and thousands of layers, achieving a richness of detail that can evoke marvel.

What is the 'Muqarna Mutation' artwork?

The 'Muqarna Mutation' is a significant artwork from Michael Hansmeyer's project. It's a 6-meter-wide, algorithmically designed muqarna installation that was featured at the Mori Art Museum’s 'Future and the Arts' exhibition from 2019 to 2020.

How was the 'Muqarna Mutation' physically created?

The 'Muqarna Mutation' was created using robotic fabrication. It comprises 15,000 aluminum tubes across 16 tiers, transitioning a central column to the ceiling. The fabrication was carried out at ROSO Coop, Feng Chia University.

What exhibition featured 'Muqarna Mutation'?

'Muqarna Mutation' was a key installation in the 'Future and the Arts: AI, Robotics, Cities, Life - How Humanity Will Live Tomorrow' exhibition. This exhibition explored the intersection of art and technology to discuss the future of humanity.

Are there physical prototypes of these algorithmic Muqarnas?

Yes, the project includes physical prototypes of algorithmic muqarnas, such as those made from gold and silver, which demonstrate the intricate forms generated by the computational design process.

How does this project connect to the historical inspiration of Muqarnas?

While using modern computational methods, the project is deeply inspired by historical muqarnas, particularly those from Safavid and Timurid Persian architecture. It honors the traditional rule-based design while pushing its boundaries with contemporary tools and techniques.

Algorithmic muqarna, computationally generated — Algorithmic muqarna protoype

Muqarna Prototype, computational design — Muqarna prototype - 32 tiers

Muqarna Mutation - inspired by Savavid architecture — Muqarna prototype - detail

Muqarna Prototype - generated using subdivision process — Algorithmic muqarna Prototype

Muqarna Design inspired by Safavid and Timurid architecture — Muqarna protoype with 3 materials

Muqarna Design, inspired by Safavid and Timurid Persian architecture — Algorithmic Muqarna with 16 tiers

Muqarnas (2019-)

Muqarnas - elaborate ornamental vaultings - are some of the earliest and most impressive examples of a rule-based architectural design. They combine architecture, mathematics, and art to form highly intricate and complex stalactite structures. The beauty of these abstract, non-figurative formations has fascinated people throughout history.

Today, advances in computational design and digital fabrication invite us to revisit these typologies. How can computation and robotic fabrication bring the splendor of such a rule-based geometric art into the future? Can the computer help us to explore new and unseen muqarna formations? In this project, the computer becomes a tool for search and exploration, a partner in our quest for the hitherto unseen. It allows us to create objects of exceptional breadth and depth: endless permutations of designs with a richness of detail that can once again evoke marvel, curiosity and bewilderment.

Historical Archetypes

Muqarnas originated in the 11th century under the Seljuk dynasty, initially serving as structural transitions between the square base of a building and the circular foundation of its dome. Composed of stacked, overlapping horizontal layers, these elements gradually evolved from purely functional supports into intricate sculptural forms. Over time, the connections between layers became more articulated, giving rise to an elaborate ornamental system that transcended structural necessity.

By the peak of their development, muqarnas had become a hallmark of Islamic architecture, adorning the interiors and portals of mosques, madrasas, shrines, and palaces. Their thousands of meticulously arranged facets create a mesmerizing saturation effect, often likened to a star-filled sky. Some interpretations also associate their vaulted forms with the cave where the Prophet Mohammed received his divine revelations, adding a layer of spiritual symbolism.

Over the centuries, artisans devised countless geometric variations of muqarnas, many displaying astonishing ingenuity and complexity. Despite their diversity, all muqarnas share the same fundamental principle: a stepwise transition between two geometries, achieved through a sequence of tiered layers. These tiers can be represented in two-dimensional ceiling plans as contour lines, revealing their underlying logic.

While the construction principle remains simple, historical muqarnas ceilings often feature elaborate geometric patterns, including nonperiodic tilings with multiple rotational symmetries. It is this interplay—between straightforward horizontal layering and intricate planar designs—that lies at the heart of muqarnas' enduring appeal, captivating observers for centuries with their harmonious blend of mathematical precision and artistic splendor.

Algorithmic Composition

How can we formalize a simple yet open-ended algorithm to design intricate muqarnas—and could it unlock entirely new, unseen formations?

This project explores an algorithmic approach to generating muqarnas ceiling plans through selective recursive subdivision.

Starting with two contour lines (representing the top and bottom outlines of a muqarnas), the algorithm iteratively subdivides the space between them into increasingly refined tiles. Crucially, subdivision is not uniform—each tile’s geometric and topological properties determine whether it splits further, enabling both global diversity and local variation within a single design.

Once subdivided, contour lines connect tiles across tiers, and the 2D plan is extruded into three-dimensional form.

Beyond replicating historical muqarnas, this method can generate radically new designs. While traditional muqarnas comprise hundreds of tiles arranged in dozens of layers, computational iteration can produce millions of micro-tiles—so dense that individual polygons dissolve into fluid, continuous surfaces. At this scale, the stepped transitions of classical muqarnas vanish, replaced by undulating concave and convex geometries that no longer require modular embellishment. The result is a fusion of ancient logic and unprecedented form.

Ceiling plan produced through selective subdivision

Algorithmic muqarna with gilded material — Algorithmic muqarna protoype

Pentagonal lgorithmic muqarna, computationally generated — Pentagonal muqarna protoype

Triangular algorithmic muqarna, computationally generated — Triangular muqarna protoype

Materialization:

Muqarna Mutation at Mori Art Museum

How can these algorithmic muqarnas be brought out of the computer into the real world? For their 2019-2020 Future and the Arts exhibition at Mori Art Museum in Tokyo, the curators commissioned a Muqarna Mutation: an algorithmically designed, robotically fabricated, 6-meter wide muqarna to be installed in a central exhibition room. The project explores how - in the context of the fourth industrial revolution - computation and robotic fabrication can bring the splendor of such a rule-based geometric art into the future.

Muqarna Mutation uses the selective subdivision algorithm described above to produce a geometry that connects a massive pre-existing column at the center of an exhibition room to the room's ceiling. The algorithm generates hundreds of thousands of tiles set among sixteen tiers to create an extragavant ornamental transition from column to ceiling.

A mass-produced industrial product, extruded aluminum profiles, is turned into an elaborate ornamental structure through a radical use of information technology: an algorithm successively defines an intricate form, and robots refine and ennoble simple tube elements into an ephemeral ensemble. The resulting structure transcends the historical typology into something new and unseen.

Standing beneath the muqarna, visitors are struck by a mix of bewilderment and curiosity: a disorientating sensory overload partially obscures the underlying compositional logic. Patterns are readily discernible as one changes perspectives, only to disappear again amidst the endless reflections.

Muqarna Mutation, Mori Art Museum, Future and the Arts exhibition, 未来と芸術展 — Kyungsub Shin

Muqarna Mutation at Mori Art Museum

Muqarna Mutation, Mori Art Museum, 未来と芸術展, Future and the Arts exhibition, Michael Hansmeyer — Kioku Keizo

Muqarna Mutation - Future and the Arts exhibition

Muqarna Mutation detail, Mori Art Museum, Future and the Arts exhibition, Michael Hansmeyer, 未来と芸術展 — Kioku Keizo

Muqarna Mutation - tube detail

Muqarna ceiling plan Mori Art Museum, Future and the Arts exhibition — Muqarna ceiling plan, at Mori Art Museum

Mori Muqarna Design Concept

The basis of Muqarna Mutation is a massive, pre-existing 1.6m wide structural column situated at the center of one of Mori Museum's exhibition rooms. Rather than contructing a muqarna in the constrained space between the column and the room's walls, the column itself is used as the origin of the muqarna. Muqarna Mutation creates a transition between this column and the room's ceiling.

A selective subdivision algorithm uses the column's outline and the ceiling's contour to produce a muqarna plan with hundreds of individual tiers, and millions of tiny facets. The algorithm refines these countour lines to create a vast landscape with seemingly endless detail, alternating between stalactives and concave formations. This initial design is depicted in the concept development images.

For fabrication, a mass-produced industrial product - extruded aluminum profiles - is robotically refined and ennobled into a elaborate ensemble. Tiling patterns are articulated as 15,000 individual aluminum tubes.

Reflections and interferences between the shiny tubes create a saturation effect that mirrors the muqarna's historical predecessors. Patterns appear and disappear as one moves beneath it and changes perspectives.

Initial algorithmic muqarna design — Initial algorithmic design

Muqarna ceiling plan in Mori Art Museum exhibition room — Position within exhibition room

Muqarna Mutation - initial ceiling plan — Initial ceiling plan

Muqarna Mutation, plan with tiers, tiles, and tubes — Plan with tiers, tiles and tubes

Robotic Fabrication

Fabrication of the Muqarna Mutation's took place at the ROSO Coop laboratory of Feng Chia University, Taiwan, under the expertise of Yu-Ting Sheng and Shih-Yuan Wang.

The muqarna was partitioned into sixteen horizonal tiers, and these in turn were divided into 40 separate components to facilitate transport and assembly. Individual tiers were robotically milled out high-density EPS. In a second step, thousands of holes of different depths and diameters were robotically drilled into the tiers. Separately, a smooth plastic foil was laser-cut and attached to the tiers to improve the surface quality. To articulate the the tiles of the original design, 15,000 individual hollow aluminum tubes were inserted into the tiers and glued into place. Specific tubes were custom fabricated in order to minimize their weight.

The completed muqarna has a surface area of 24m² and a height of 2.4 meters.

Muqarna component (1 of 40) with tubes — Muqarna component with embedded tubes

ROSO Coop lab — Milled muqarna component with tiers

Tube detail — Tube interference patterns

Team and Partners

Fabrication Team

Lead:		Yu-Ting Sheng 盛郁庭 (Feng Chia University) Shih-Yuan Wang 王識源 (National Chiao Tung University) Meng Hao 孟浩 (RoboticPlus)
Structural support:		Chen-Tung Chen 陳建同 (YUMU) Kuan-Fan Chen 陳冠帆 (FA.S Studio)
Fabrication Assistants:		Fei-Fan Sung 宋非凡 Che-Wei Lin 林哲蔚 Wei-Tse Hung 洪維澤 Yu-Hsuan Pang 龐宇軒 Chung-Chieh Cheng 鄭中杰 Yi-Heng Lu 陆亦恒 Nai-Wei Lai 賴乃葳 Chieh-I Liu 劉婕怡 Chang-Chin Lee 李長錦 Shih-Kai Fan 范士凱 Yu-Syuan Wei 魏雨萱 Ching-Yun Tseng 曾慶芸 Ying-Yu Chen 陳盈佑 Yu-Wei Cheng 程昱維 Qin-Fei Liu 劉沁霏 Yen Heng Cheng 鄭硯恆

Partners and Sponsors

• ROSO COOP - Feng Chia University

• Graduate Institute of Architecture - National Chiao Tung University
• RoboticPlus 大界機器人
• Nan Pao Resins Chemical
• YUMU Manufacture and Research
• A.S. Studio 原型結構工程顧問有限公司

Muqarna Mutation is a commission by the Mori Art Museum, Tokyo, for its Future and the Arts exhibition [未来と芸術展]. It premiered in November 2019.

Algorithmic muqarna protoype

Muqarna prototype - 32 tiers

Muqarna prototype - detail

Algorithmic muqarna Prototype

Muqarna protoype with 3 materials

Algorithmic Muqarna with 16 tiers

Muqarnas (2019-)

Muqarna prototype with tubes

Muqarna prototype with tubes

Muqarna prototype

Historical Archetypes

Algorithmic Composition

Algorithmic muqarna protoype

Pentagonal muqarna protoype

Hexagonal algorithmic muqarna

Triangular muqarna protoype

Algorithmic muqarna protoype

Muqarna Mutation at Mori Art Museum

Muqarna Mutation at Mori Art Museum

Muqarna Mutation at Mori Art Museum

Muqarna Mutation - Future and the Arts exhibition

Muqarna Mutation - tube detail

Muqarna Mutation - 未来と芸術展

Muqarna Mutation - tube detail

Muqarna ceiling plan, at Mori Art Museum

Mori Muqarna Design Concept

Initial algorithmic design

Position within exhibition room

Initial ceiling plan

Plan with tiers, tiles and tubes

Robotic Fabrication

Muqarna component with embedded tubes

Milled muqarna component with tiers

ROSO Coop lab, Taichung

Trial assembly - outer components

Tube interference patterns

Team and Partners

Fabrication Team

Partners and Sponsors