Archives for the Month of April, 2015

The Logic of Crystals – William T. Astbury & Kathleen Yardley’s Space-group Diagrams

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

William T. Astbury and Kathleen Yardley’s 230 Space-group diagrams, published in 1924, form a complete notation of all possible atomic lattice configurations in crystals (not including quasi-crystals). The figures formed the basis for what eventually became the International Tables for X-ray Crystallography. A crystal is three-dimensional tessellation of ‘unit-cells’. Each cell is a fundamental pattern of atoms or molecules repeated, rotated, folded. Depending on its symmetry, the unit cell of any given crystal can be classified according to one of those 230 space groups.

Deciphering these geometric sigils, without fundamental knowledge of their crystallographic logic, may be tricky but the plates have a rigorous aesthetic that stands up by itself. Non textual oblique strategists may already be mapping these tridimensional diagrams to create irrational marriages; for rendering micro-crystalline morse-code music or for use as guides to direct their psychogeographical drifts. The 230 space-diagrams designed to navigate crystal space might also be used to negotiate space taxonomies of other kinds.

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

Well aware of hidden language of crystals, Shea Zellweger employed their lattice configurations as a model for his Logic Alphabet – ‘a set of symbols that systematically represents the sixteen possible binary truth functions of logic’. Zellweger arranged the letter-shapes according to the structure of a crystal so that their interrelating symmetries could more easily visualised and manipulated.

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

Inspired by X-ray crystallography, and under the direction of Helen Megaw (a crystallographer who determined the structure of the ice crystal), the Festival Pattern Group developed textiles based on the atomic lattice of insulin, china clay, and hemoglobin for the Festival of Britain in 1951. In 2008, the Wellcome Collection, in London, curated an exhibition on the Festival Pattern Group called ‘From Atom to Patterns’.

Further Reading:
Logic Alphabet Project – Shea Zellweger

Related Posts:
The Melodies and Megaliths of Pseudocrystalline Terrains

The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] (source unknown)

The self-similar, cascading architectural forms found in Hindu temple architecture appear to have been pieced together by a hyper-industrious Minecrafter hooked on Hofstadter. Jagged waves of blocky ornamentation, rhythmically repeating, create diminishing echo’s of the temple’s form; tiny versions of itself repeating towards a proposed infinity. Baroque three-dimensional Cellular Automata. Cantor Set masonry. Malevich’s Architectons upscaled and iterated to the nth degree, often smothered with a teeming mass of deities and denizens, each one competing for your retina.

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] – RM Nunes

It’s not just that these temples appear to be algorithmically generated, the ancient Vastu Sustra texts provide procedural rules or recipes for their design, layout and build (including the positions of ornaments). The texts transmit recursive programs, by verbal instruction, to masons so that according to Kirti Trivedi, the Hindu Temple becomes a model of a fractal Universe. A model which represents ‘views of the cosmos to be holonomic and self-similar in nature’. The idea of fractal cosmology is no stranger to western academia. In 1987 the Italian physicist Luciano Pietronero argued, in his paper, that the Universe shows ‘a definite fractal aspect over a fairly wide range of scale’ based on correlations of galaxies and clusters, their spatial distribution and average mass density.

‘According to Hindu philosophy the cosmos can be visualised to be contained in a microscopic capsule, with the help of the concept of subtle element called ‘tammatras’. The whole cosmic principle replicates itself again and again in ever smaller scales’ – Kirti Trivedi

Indian Temple FractalsYellamma Temple [Karnataka] – Paul Prudence

Indian Temple FractalsArchitecton Series – Kazimir Malevich [1923]

Indian Temple FractalsTemple Plan for Barwasagar Temple [Uttar Pradesh] from Geometry Measure in India Temple Plans

The initial temple plan is based on a grid form known as the Vastu-Purusha Mandala. Tellingly Trivedi remarks in his paper that the Vastu-Purusha Mandala is ‘not a blueprint for a temple, but a ‘forecast’, a marking of the potential within which a wide range of possibilities are implied’. The significance here, should not be underestimated. A ‘potential for possibilities’ within a predefined rule-set predisposes architecture to be governed by a degree of emergence. While emergence in parametric architecture arrived, recently, with computers and algorithms, India has been enacting emergent masonry for thousands of years thanks to the open rules of the Vastus Sustra.

Indian Temple FractalsShweta Varahaswamy Temple [Karnataka] – Paul Prudence

Using a system of measurement called the ‘Tala’, dimensional relationships of proportions rather than exact structural specifications are defined. Initial decisions (why not call them algorithmic seeds?) combined with rule sets are used to define the final outcome of the building. The ‘Tala’ system is scale invariant, just like fractal mathematics, so that a building of any size can be created, and decorated without compromising the model of self containment. The temple, as a whole, is built by interweaving fractalization processes with repetition and superimposition. An example of a typical recursive instruction, verbalised, is:

The layer of prahara (projection) will be above the chadya (eave of the roof). This is to be repeated again and again on the spire over the spire. A fraction of the prahara is to be constructed and again the spires are to be constructed. Each of the upper spires will be sprouted out with a measurement equal to half the size of the lower spire – Ksirarnava, 7.113

Indian Temple FractalsSri Meenakshi Amman Temple [Tamil Nadu] – Paul Prudence

The Kandariya Mahadev, in Madhya Pradesh, is one of the best examples of recursive temple architecture in India. The rising towers (Shikhara) of this structure are said to mimic the forms of mountains which are themselves self-similar. Shikhara literally translates to the word mountain.

Inspiration by way of a recent trip (one of many) to Karatanka, Tamil Nadu and Kerala.

Further Reading:

The Hindu Temple is a Model of a Fractal Universe – Kirti Trivedi [1993]
Infinite Sequences in The Constructive Geometry of 10th Century Hindu Temple Superstructures – Sambit Datta [2010]

Related Posts:

Stanley Tigerman & G. T. Crabtree – The Formal Generators of Structure
Breed – Driessens & Verstappen: Evolutional Diffusion Lattices
Yuri Avvakumov – Agitarch Structures: Reconfiguring Utopia