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Category Archives: Aperiodic Tiling
Numerical Separators
With a base 10 place value number system, Britain and America use the period as the radix symbol, to separate integers and decimals, and use a comma to separate groups of digits; for example, they would write 3,200,100.56 Other Europeans … Continue reading
Posted in Aperiodic Tiling, Architecture, Classification, Enumeration, Logic
Tagged Classification, Enumeration, Logic
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The Long and the Short
A yearout student Tom Kirby emailed an office of 200 people asking what the convention was for beyond and behind dotted line styles. No one knew. Online searches didn’t prove very helpful so in one of those mad delightful collective … Continue reading
Posted in Aperiodic Tiling, Architecture, Frozen Music, Rhythm
Tagged Aperiodic Tiling, Frozen Music, Rhythm
5 Comments
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
2 Comments
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
Aperiodic Tiling
This closely follows “Tilings and Patterns” (Grünbaum and Shephard, 1987), but uses coloured diagrams rather than their monochrome ones. In some ways this is simply a catalogue of aperiodic tilings, their various forms and some indication of their uses, but my interest … Continue reading
Posted in Aperiodic Tiling, Architecture, Geometry
Tagged Aperiodic Tiling, Geometry, Tiling
6 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
Quasicrystals and Aperiodic Tiling
In 2011 Dan Shechtman was alone awarded the Nobel Prize in Chemistry for the discovery of quasicrystals. Shechtman found in 1982 that atoms in a crystal could exhibit 5 fold symmetry packed in a pattern that did not repeat itself; analogous … Continue reading