What might the patterns of urban sprawl look like if humanity were to survive another thousand years or so? Artist Tom Beddard envisions fractal formations seemingly cut right into the earth, broken up by the occasional sky-high tower or curving superstructure. The architecture in this futuristic vision entitled ‘Aurillia’ ranges from bleak industrial scenes to incredibly complex city centers, all created using a fractal formula called Mandalay.

The London-based artist, who earned a PhD in laser physics before moving on to design and web development, used the Fractal-lab tool that he built himself to render the images. Fractals in visual form are generally characterized by obvious patterns, but with this formula, the resulting aerial views have a surprisingly organic look.

“What I found particularly interesting was the mix of architectural forms that could be found when certain parameter combinations create structural resonances,” Beddard told The Creators Project. “The curved domes are due to the Mandlebox sphere folding effect and the towers result from the different fold scaling of individual axes.”

We’ve seen some amazing applications of fractals and parametric designs in architecture and furniture designs, from mobile pavilions to fantasy cities, but nothing on quite this large of a scale. Check out aerial views of real-life suburban complexes and you’ll see that these patterns aren’t all that far from the patterns we’re already creating with urban development.

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.

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.

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 scrips 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!”

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.

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 travelers 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 colorful glass to catch the light.

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.

Next Page - Click Below to Read More:
Algorithmic Architecture 14 Fractalparametric Structures

Geometry lies at the core of every design process, and as computer-aided design becomes more common, the patterns that can be found in architecture, furniture and home decor grow increasingly complex. The use of fractal geometry, in which a geometric pattern is repeated at smaller and smaller scales to produce irregular shapes and surfaces, is among the most visually interesting. Here are 12 fractal (and fractal-inspired) designs, from tables to the canopy over a train station.

Fractal Table by Platform Wertel Oberfell

(images via: platform-net.com)

Mimicking fractal growth patterns found in nature, the Fractal Table by Platform Wertel Oberfell features legs that resemble tree trunks that divide over and over again until they’re dense enough to form a patterned surface.

Homune Table by Michael Young

(images via: design boom)

36 individual hand-blown glass fractals – six forms repeating six times – come together in this amber-colored geometric table by Michael Young. Says the designer, “over the years we have experimented with fractal structures creating endless constructions, not art but design experimentation,  studies into the unknown and transpired this research into the new lasvit glass table. we discovered that by blowing glass into only one metal tool and cutting it at different lengths, we could make logical and functional structures, the first thing being this special edition table.”

Ornamented Columns by Michael Hansmeyer

(images via:  design boom)

These columns are so complex, at first they don’t seem as if they could possibly be real. Michael Hansmeyer first designed his ‘ornamented columns’ using algorithms and subdivision processes that result in incredibly varied topographies. The designs were then created in three dimensions using 1mm grey board sheets that were individually cut using a mill or laser, then stacked together on poles that run through the core.

>Cellscreen by Korban/Flaubert

(images via: korbanflaubert)

Made of anodized aluminum, this room screen by Korban/Flaubert takes its inspiration from the fractal shapes of honeycomb.

Diffusion Vessels by David Sutton

(images via: dezeen)

These unusual vessels were created by digitally fabricating the fractal growth patterns of natural phenomena like lightning and snowflakes through a process called ‘Diffusion Limited Aggregation’.

Embedded Project by HHD_FUN<

(images via: hddfun)

Architecture firm HHD_FUN created a pavilion in Beijing that features a pattern based upon a triangular fractal pattern. The faces of the pavilion were designed using a recursion algorithm, sub-dividing or ‘cracking’ each triangle into smaller and smaller triangles. At each ‘cracking’, new triangles are raised from the surface to create a three-dimensional pattern.

Absent Nature by Arik Levy

(images via: dezeen)

More than a thousand light tubes make up ‘Fractal Cloud’, a light installation by Arik Levy. “In the shadow of the Fractal Cloud light an enormous hexagonal ring of powerful light has been created from over one thousand light tubes woven onto another to become a single light-emitting textile projecting two small ricochets, one in colour and one in warmer white light.”

Fractal LED by Arik Levy

(images via: dezeen)

Arik Levy also completed this ‘Fractal LED’, another in his fractal LED light series.

Lisbon Oriente Station by Santiago Calatrava

(images via: wikimedia commons)

Lisbon’s Oriente Station by Santiago Calatrava is a dazzling example of mathematically inspired architecture. Calatrava is known for designs that are often rooted in natural patterns and forms, particularly sea life and birds.

Helios House

(images via: wikimedia commons)

Its design may not technically be fractal, but the Helios House gas station in Los Angeles definitely has the look of a mathematical pattern to it, with its faceted stainless steel facade.

Fractal LiveBook

(image via: design boom)

This unusual design is a notebook computer that can be broken into smaller pieces, each of which is a reduced-scale copy of the whole. Says designer Pedro Calle, “Fractal LIVEBOOK is everything you need, it can be split into pieces each of which can work individually as laptops, pads, music players and tweak them with apps and widgets. It also can work together as a console with different touch-screens with programs, menus, tools, palettes, brushes and audio samplers, separating physically the workspace. Find all the fun on customizing your LIVEBOOK’s fractals, share them with your friends and enjoy making the digital realm a more analogous experience.”

Hive Mind Office Table

(images via: omcdesign)

Offering more privacy and adaptability, and certainly better looks, the ‘Hive Mind’ office desk system is an alternative to conventional cubicles that can create fractal working spaces in various configurations.