14 COMPLEX MATH-BASED ARCHITECTURES

Algorithmic Architecture: 14 Complex Math-Based Structures
By Steph, Web Urbanist, 26 February 2014.

Mathematics are more integral to architecture than ever before, and as the methods of designing structures grow more complex, so do the calculations. As these fractal and parametric designs - both built and fantasy - prove, the only limit to architecture based on mathematical algorithms are those of physics and materials, and with the advent of 3D printing and other advanced construction techniques, the world of amazingly complex architecture just keeps getting bigger and bigger.

1. Parametric Party House

Built for Copenhagen Distortion, a summer festival that draws thousands into the city’s streets and clubs for all-night dance parties, this mobile parametric pavilion aims to “give architectural expression to this Dionysian experience.” Designed and built by experimental technology and acoustics programs from three universities, the pavilion rotates and moves like a piece of fabric despite the fact that it’s made up of 151 hinged plywood triangles finished in a reflective copper.

2. Intricate Fractal Fantasy Architecture by Tom Beddard

Tom Beddard’s fantasy architecture is far from realistic; instead, it’s an exploration of just how complex structures derived from algorithms can get and still be recognizable as potential human habitations and cities. Beddard makes some of the scripts he uses to create his works available on his website. Says the artist, “For me the creative process is writing my own software and scripts to explore the resulting output in an interactive manner. The best outcomes are often the least expected!”

3. L-Systems by Michael Hansmeyer

“For centuries architects have been inspired by nature’s forms and geometries,” says Michael Hansmeyer, a designer who produced the world’s first 3D-printed room as well as some amazingly complex fractal columns. “It is only in the past decade that much of the underlying logic, mathematics and chemistry of nature’s forms has been better understood. In the late 1960′s, the biologist Aristid Lindenmayer proposed a string-rewriting algorithm that can model simplified plants and their growth processes with an astounding ease. This theory is now known as L-Systems. This project examines whether this algorithm can open up possibilities in the field of architecture.” See more L-Systems in architecture at Hansmeyer’s website.

4. SOM Mumbai Airport Canopy

A fractal roof canopy tops off a terminal at Mumbai’s Chatrapati Shivaji International Airport, modernizing a complex that accommodates 40 million travellers every year. The design visually references the form of vernacular Indian pavilions with thirty mushrooming columns. The kaleidoscopic canopy extends across the arrivals roadway and is embedded with small disks of colourful glass to catch the light.

5. Fractal-Based Sky Habitat for Singapore

This fractal design by Moshe Safdie makes the absolute most of a small land footprint with a high-density 38-story sky habitat integrating stepped balconies that democratize views and private outdoor space.

Envisioned for Singapore, the tower is porous to light and air to maximize air movement in the tropical climate, and features a series of sky bridges containing parks and swimming pools.

6. Spiral Sculpture by Daniel Libeskind, Spain

‘Beyond the Wall’ is a sculptural installation representing the infinite possibilities of a spiral, located outside the world headquarters of the Cosentino Group in Almeria, Spain. Studio Daniel Libeskind designed the volume as a non-repeating pattern that ‘creates a mathematical mosaic’ in the shape of a polycentric spiral.

7. Bicentennial Arch Mexico City

This proposal for a national competition to design a memorial commemorating the Bicentennial of Mexican Independence was made to lose. In fact, designers Michel Rojkind, Alejandro Hernandez and Arturo Ortiz intentionally gave their submission a dystopian feel to protest what they saw as a waste of intellectual and economic resources on an archaic project. The drawings for the fractal arch design include depictions of class inequality and inevitable problems like traffic congestion and informal vendors. “What are we going to celebrate? That the streets in the city are a chaos? That has been years since the last time there was a competition to do social housing in Mexico? That the people takes 3 hours to get to work? That the governors and political class, aiming to be remembered propose a project that will cost millions of pesos to execute it in a ridiculous time and closing Reforma and Circuito Interior (2 of the main avenues in Mexico City)?” Rojkind asks.

8. Stockholm Library of the Future

Mathematical patterns provide the striking focal point of ‘the library of the future,’ a design for a new Stockholm City Library by Emergent Architecture. Primary Tom Wiscombe says the design is “a linking mechanism at the urban scale” to network disciplines and people in an urban setting. The design is cellular in nature. Says the architect, “Cells are understood in terms of their interactivity in aggregate form, and their potentials for generating emergent structural and organizational effects. Cells vary in scale, thickness, and density, adapting toward performance and materiality without breaking their smooth formal gradient. A Voronoi algorithm was used in combination with hands-on manipulation of the patterns in order to produce variability.”

9. Melbourne’s Federation Square by LAB Architecture Studio

Three parametric structures make up a new (and somewhat controversial) mixed-use complex in Melbourne’s Federation Square.

Designed by LAB Architecture and Bates Smart, each structure is highly complex and offers a literal sharp contrast to the adjacent historic architecture. The non-classical geometries that make up each distinct building are based on concepts of fields of force and focus.

10. Fractal Geometry Tower

Envisioned for the edge of a pier in Manhattan’s Battery Park, ‘Fractal Geometry Tower’ by Margot Krasojevic is designed to reflect light in such a way that you're not entirely sure whether it’s just an optical illusion, using both “physical hyperbolic geometries and their fractal reflections.” The designer explains, “With regard to the Tower, the perceived space is translated and continually morphed as a result of the surface renderings and reflections, whose boundaries and physical transitions are non-static, thus creating a dynamic series of dimensions. The reflecting surfaces have a Hausdorff dimension greater than its topological dimension, with the aim of presenting an infinite number of geometric iterations of an infinite length while the area remains finite. The surface reflections, however, are too irregular to be easily described using a traditional Euclidean geometric language. Both these criteria are characteristics of fractal as a complex geometric object.”

11. Tetrahedron  Skyscraper, San Diego

The designers of the Tetrahedron Skyscraper looked at the legacy of ancient forms and simple geometry to identify the shape that encloses space in its most simple form.

This shape, which is simply four times the area of a single face, can be found in virtually all architecture including the pitched roofs of suburban homes. In this tower, each ‘tetra’ is a single condominium unit.

12. Parametric Skyscraper, Beijing

How can the floor plates and facade of a skyscraper be transformed according to different parametric programs? The designers of the ‘Lattice Towers’ project for China use “a series of tectonic manipulations” to change the appearance of the building. Its curving shape varies dramatically depending on your viewpoint.

13. Fractal Bamboo Pavilion

Using the basic unit of the Sierpinski Triangle, a pure fractal form, this fractal pavilion design achieves structural stability using nothing but bamboo trusses and latticework covered in acrylic glass.

14. Inflatable Yorkshire Diamond Pavilion

This might just be the most complex inflatable structure ever designed. Various Architects created the Yorkshire Diamond Pavilion with inflatable tubes forming a diamond-lattice structure. While it looks like a box from the outside, the interior is a cavernous ‘excavated’ space reminiscent of the town’s coal mines. The double-layer skin lets in light and air, and enable streams of colourful light to emerge when the structure is lit up at night.

[Source: Web Urbanist. Edited.]