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Danzer Packing

http://www.archdaily.com/tag/cecil-balmond/

The Danzer Light is an innovative solution to boring light fixtures. The light is made out of 180 triangles that can be rearranged to create different shapes. The inspiration for the Danzer Light is based on Ludwig Danzer's mathematical principle on "aperiodic tiling."

The light fixtures are essentially wireless due to the current that is conducted through the aluminum structure of the triangles. The coolest part about the Danzer Light is the flexibility of the triangles--because every surface has a shared space, the light has endless possibilities for reconfiguration.

The three-dimensional analogs of the planar penrose tilings and quasicrystals.

Balmond Studio

Combining studies in chemistry, mathematics and architecture, Balmond opened up new architectural routes, making what was once impossible, possible. He has developed a means of handling extremely complex architectural compositions. Inspired by natural structures, Balmond has created algorithms and new geometries, designed to free up architectural forms.

http://balmondstudio.com/

Reference

an exploration of the aperiodic space-filling Danzer tiling system as a generative tool for the tower design started in earnest.

http://www.wallpaper.com/architecture/element-by-cecil-balmond-tokyo/4331

http://balmondstudio.com/

http://landartgenerator.org/blagi/archives/1043

http://www.sh-o.us/project/super-tall-performance-and-atmosphere/

http://eprints.ucl.ac.uk/4982/1/4982.pdf

The four tetrahedral in their first iteration, and the reordering of the vertices that their subdivision produces, in order to maintain the topology of the produced tiles

‘Three-dimensional analogs of the planar penrose tilings and quasicrystals’ (Danzer, 1989). The four initial tiles are tetrahedral of types A, B, C and K and are defined through the lengths of their ordered edges. All of these lengths are proportional to the golden ratio τ = (1+√5)/2.

illustration of the basic inflation process for the Danzer aperiodic set.

(On the left) The three prototiles of the aperiodic set and their edge matching conditions.

(In the middle) The first iteration of the inflation process involves decomposing each prototile into a collection of tiles.

(On the right) The second iteration involves further decomposing each tile based on the rules from the first iteration. Large tilings are formed as this iterative process is repeated.

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