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Category Archives: Tiling
William Tutte’s Hidden Past
If William Tutte is remembered at all by architects, it is for his contribution to solving the problem of Squaring the Square . (Tutte 1958) A solution using Graph Theory and Kirchhoff’s Laws for electrical flow in wires that was subsequently used in Philip … Continue reading
Posted in Architecture, Design Methods, Geometry, Logic, Tiling
Tagged Aperiodic Tiling, Architecture, Design Methods, Geometry, Logic, Tiling, Turing Machines
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Aesthetics of Aperiodic Tilings
Wang tilings seem to me to be visually more interesting than their plain or decorated aperiodic tiling generators. The various versions of the same Penrose P2 tiling below all look very uniform, with their randomness hardly registering, whilst the randomness … Continue reading
Posted in Aesthetics, Aperiodic Tiling, Architecture, Tiling
Tagged Aesthetics, Aperiodic Tiling
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Find Your Own Space
A randomly distributed sets of points can be considered as the lowest state of architectural order; the placing of the simplest object, a point, with the least degree of structure, being randomly placed. Well distributed point sets are important in … Continue reading
Posted in Aesthetics, Aperiodic Tiling, Architecture, Geometry, Tiling
Tagged Aesthetics, Aperiodic Tiling, Architecture
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Wang Tiles and Turing Machines
Wang pointed out that it is possible to find sets of Wang tiles that mimic the behaviour of any Turing Machine (Wang 1975). A Turing machine can compute all recursive functions, that is functions whose values can be calculated in … Continue reading
Posted in Aperiodic Tiling, Architecture, Geometry, Tiling, Turing
Tagged Aperiodic Tiling, Architecture, Geometry, Tiling, Turing Machines
22 Comments
Wang Tiles and Aperiodic Tiling
Wang originally conjectured that no aperiodic tilings could exist. Wang was interested in the decidability of the Tiling Problem; it is said to be decidable if there exists an algorithm which will yield a solution for any given set of prototiles … Continue reading
Posted in Aperiodic Tiling, Architecture, Geometry, Tiling
Tagged Aperiodic Tiling, Geometry, Tiling
13 Comments
Periodic and NonPeriodic Tiling
The concepts of periodic and nonperiodic tiling are defined so as to clearly distinguish them from aperiodic tiling; the subject of a future post “Aperiodic Tiling”. Informally a tiling (of the 2D Euclidean plane) is a collection of subsets of … Continue reading
Posted in Aperiodic Tiling, Architecture, Geometry, Tiling
Tagged Aperiodic Tiling, Architecture, Geometry, Tiling
4 Comments