The Dark Web of Crystallographic Crochet

crystallographic crochet

Nearly every source of attribution for old crochet patterns found on the web remains a mystery. There exists a dark web of pattern swapping enthusiasts fostering a contagion spread that conceals its origin. But one source identified is the old Russian language Duplet Magazine – worth singling out for its graphic ordering of patterns in optical monochrome cells configured to its own space-filling logic. Close-knit windowpanes create a comic strip story of evolving symmetry – a biological taxonomy of tiny skeletal organisms – Haeckel’s Radiolaria or Baricelli’s number-shaped organisms? Duplet really leads a double life as a handbook of space-group morphologies for symmetry fetishists.

Note: At some-point we will revisit that story about KGB spies using crochet to encrypt secret cold war messages.

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

crystallographic crochet

Reverse engineer crochet patterns and we find all those familiar mathematical forms dear to the modern visualist – grammar-tree systems; iterative branching structures; fractals; symmetry groups – hook and needle code embedded as form. Spot the space-filling curves and the hyperbolic plane in the images above. Here’s a small selection of links to literature on algorithmic crochet and knitting techniques:

Evolution of Lace Knitting Stitch Patterns by Genetic Programming – Anikó Ekárt

Algorithmic Form Generation for Crochet Technique

Knitting for Fun: a Recursive Sweater

Design of a Nature-like Fractal Celebrating Warp-knitting

Computer-Aided Weaving:From Numerical Data to Generative Textile

Algorithmic Form Generation for Crochet Technique

Related Posts:

René Binet – Esquisses Décoratives & the Protozoic Façade of Porte Monumentale

Nils Barricelli’s 5 Kilobyte Symbiogenesis simulations and ‘molecule shaped numbers’ – A precursor to DNA Computing

The Hyperbolic Crochet Coral Reef & other non Euclidean Miscellany

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Selected Tweets #26 – Gridcollages, Chalcopyrite & The Music of Trains

Danny WillsCultivating the Map – Danny Wills

Selected tweets from @MrPrudence

Torvaianica – Josef Dabernig [1984] Translating the Torvaianica in Lazio via a² + b² = c² to create data notations.

Glossolalie 61 and other graphic Scores – Dieter Schnebel.

Fascialis 20% @wblut is re/deconstructing 3D anatomy.

Rento Van Drunen’s Gridcollages – abstract renditions of complex geometries & spatial modularities.

Modular geometric transforms of a plan system – Walter Netsch [Progressive Architecture 54 April 1973].

The Burning Ship Fractal discovered by way of Rossler Attractors and El Naschie’s ‘undisciplined numerological’ E-infinity theory.

“Let us Calculate!”: Leibniz, Llull, and the Computational Imagination.

Philly Area Highways – 1972. Design constraints and stylisations of map making expressed as Mondrian-isms.

FascialisFascialis – Frederik Vanhoutte

Cultivating the Map – Danny Wills. ‘Proposing that the map is also a generative tool.’

Iron Flowers, Noir Gardens – Stallating icosahedral polyhedra in monochromatic real-time.

The immense proto-brutalist neo-Gothic architecture of Hans Poelzig.

Roberto Calbucci’s studies for comic abstraction based on Martin Heidegger’s ‘The Concept of Time.’

“The fetishization of indeterminacy in the guise of a sort of complexity porn.”

Plates from The Principles of Light and Color – Edwin D. Babbitt [1878].

Score for PR–IVIII (A graphic score of cartoon sound-landscapes ) and other graphic notaion by Bogus?aw Schaeffer.

Paramecium multimicronucleata from ‘Protozoology’ – Richard Kudo [1939].

Glossolalie 61 - Dieter SchnebelGlossolalie 61 – Dieter Schnebel

Aerial tuning inductor – Rugby Radio Station, 1943-1966. Unintentional pataphysical sculpture.

Fluorite with Quartz and Chalcopyrite and other Illustrations – Arthur Smith. [1952]

The Music of Trains? Dovetailing of Train Movements, found in Graphic Presentation – W Brinton [1939].

Plates from ‘Desmids [green algae] of the United States’– Francis Wolle [1892].

Hand-painted manuscript globe of Mars – Emmy Ingeborg Brun, Denmark, [1909].

Amanita – Vic Atkinson (1974) Mushrooms + insects + cosmic library music.

Score for Kosmic Music – Wadada Leo Smith [2008].

Not a medieval alchemical diagram but a schema on optics for lighthouse engineering.

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Hiromi Fujii – Programming the Cube

Hiromi FujiiTodoroki House – Hiromi Fujii [1975]

In the 1970’s Japanese architect Hiromi Fujii neutralised his architectural projects from time, tradition and convention by using the most archetypal of all conceptual objects, the cube. Programming this minimal element through further syntactic transformations into more complex nested structures allowed his drawings retain a stark and empty elegance. Like Sol LeWitt’s combinatorial transformation drawings they have no history, or time, outside of the cold logic of their algorithmic prescription; their context is self-contained; they reference only variations of themselves.

Hiromi FujiiTodoroki House – Hiromi Fujii [1975]

Hiromi FujiiTodoroki House – Hiromi Fujii [1975]

Hiromi FujiiTodoroki House – Hiromi Fujii [1975]

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Carl Friedrich Philipp von Martius’s Historia naturalis palmarum

Historia naturalis palmarum

Carl Friedrich Philipp von Martius’s Historia naturalis palmarum – in which all known genera of the palm family are illustrated and their biogeographies described – is considered a landmark botanical survey. Taking over 27 years to complete, the three-volume work contains 240 chromolithographic illustrations which survey 2,250 km of the Brazilian Amazon and its tributaries (oh, that number thing). Many illustrations are typical of their time but what stands out among familiar stylisations are Martius’s own curious illustrations of the cross-sectional architectures of trunks and brunches. Other graphical systems clearly define the palms signature mathematical morphologies, symmetries and phyllotaxial geometries. The illustrations have been collected in the Book of Palms by H. Walter Lack published by Taschen.

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Historia naturalis palmarum

Related post:
‘You Really Do Not See a Plant Until You Draw it’

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Mead & Conway’s ‘Introduction to VLSI Systems’ – The Ornamental Heraldry of Logic Gates & Shift Registers

Introduction to VLSI Systems

The gridded geometry of VSLI diagramming celebrates the cargo cult of optimum electron flow as ornamental tribal heraldry. Part modernist weaving pattern (Gunter Stolz, Annie Albers), part tribal ornamentation – its geometric constraint aesthetic is squeezed into place by the forces of functional logic and space-filling optimisation. Introduction to VLSI Systems [1978] (PDF) contains finely coloured logic gate designs, NAND & NOR op-art and hieroglyphic transistor abstractions; and offers an early description of the circuit/microchip layout problem.

Introduction to VLSI Systems

Introduction to VLSI Systems

The creation of a geometric script to encode a symbolic layout language might be a modern day equivalent of Islamic Girih tilings or Kilim weave patterns. But rather than floral embellishments and pointed stars of the Girih tradition, VLSI constrains the symbols for input registers, logic blocks and phase clocks to best-fit space constrained by function that is devoid of any explicit aesthetic consideration. The microchip layout problems is part of a large group of much studied topological problems – and so the design of these circuits will hold clues to the solution of their more famous sibling – The Traveling Salesman Problem – and its lesser known one – The Seven Bridges of Königsberg.

Introduction to VLSI Systems

Introduction to VLSI Systems

Introduction to VLSI Systems

‘The task of the integrated system designer is to devise geometric shapes and their location in each of the various layers. By arranging predetermined geometric shapes on each of these layers, a system of the required function may be constructed..[ ]..A simple and common method of producing system layouts is to draw them by hand. This is typically done on a one lambda grid using the familiar colour codes to identify various system layers. One the layout has been hand drawn it can be translated into machine readable form, by encoding it into a symbolic layout language.’

Introduction to VLSI Systems

Introduction to VLSI Systems

Related Posts:

Microchic: Cara McCarthy’s Diagramming Microchips & Theo Kamacke’s PCB Hieroglyphics
Ulla Wiggen – Conductive Abstractions

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John Whitney’s Digital Harmony – On the Complementarity of Music and Visual Art

“The dream of visual dynamism is the same; to leave behind earthbound stasis and to fly into that liquid space of numerical architecture without gravity” – John Whitney

Digital_Harmony

John Whitney’s Digital Harmony – On the Complementarity of Music and Visual Art [1980] can now be read or downloaded at the ever brilliant Archive.org. Good news since second-hand copies of this out-of-print classic often fetch up to a few hundred pounds each on Amazon. A classic textbook for those working in audiovisual composition, the book explores technical, philosophical and conceptual aspect of software-based visual music. The computer code contained in the book is obviously well outdated but there is much to learn from Whitney’s insights into his methods for composition.

Digital_Harmony

The main tenet of the book is the idea of ‘harmonic resonance’ – that the harmony of music corresponds to the harmony of visual design. Whitney explores how graphic harmony can be generated using periodic relationships, modulation, tension vs equilibrium, interference, resonance and counterpoint in audio-visual systems. He demonstrates how interesting results from ‘the nature of patterns in time in the human perceptual experience’ can be attained without relying on the obvious mechanical synchronization of sound and image. Technologies able to translate sound into video or vice-versa (in anywhere near real-time) were scarce outside scientific laboratories in 1980 so Whitney made metaphorical and perceptual bindings using mathematical relationships in his modal systems. The book contains many full colour stills from Whitney’s films and also revealing step-by-step diagrammatic annotations to his process. He cites precursors in the field such as Len Lyre, Viking Eggeling, and Hans Richter, but he also mentions less obvious sources of inspiration such Schoenberg, Pythagoras and even Chomsky.

Digital_Harmony

“Computers will do no such thing – art is a matter of judgement not calculation / No one expects a piano to write really good music” [p124]

“Symmetries generated by kaleidoscopes and snowflakes are not unwelcome – but like medication, overuse quickly becomes overdose” [p109]

“Using chromatic scale to concatenate tonal reflection upon tonal statement, at exactly the right time, that is how Debussy gave elegance to the shape of time” [p85]

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Digital_Harmony

Related Posts:

Permutations & Arabesque – John Whitney
Emma Kunz – Cardinal Points

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Selected Tweets #25: Sunspots, Fulgurites & Pathological Fractals

Georg_von_WellingIllustrations from Opus mago-cabalisticum et theologicum – Georg von Welling [1719]

Selected tweets from my Twitter stream @MrPrudence

Group of Sun Spots and Veiled Spots – E. L. Trouvelot [1873].

Chromatic Drawings – Ivan Wyschnegradsky.

Polyomino II – Jose Sanchez and students. Combinatorial patterns generated in Unity3D.

Illustrations from Opus mago-cabalisticum et theologicum – Georg von Welling [1719].

Hacker Slang and Hacker Culture – AI Koans, Hacker Folklore in The Jargon File, circa 2000.

A Cognitive Computation Fallacy? Cognition, Computations and Panpsychism – John Mark Bishop.

The Analog Art – Joost Rekveld traces the history of analogue computing leading to his current film work #59.

No Code: Null Programs – Nick Montfort [PDF]. The null program or lack of code as a functioning program.

Marginal, Local and Time-Bound – Sydney Lévy [PDF]. Edgar Allan Poe, Charles Babbage & the machinations of the mind.

Hadopelagic – Hideki Inaba. Fischingeresque time and motion study in candy coloured pop.

CarpentryIllustration from Carpentry : Being A Comprehensive Guide Book for Carpentry and Joinery – Nicholson, Peter, [1848]

EKO ComputeRhythm – a drum machine that used punched paper cards from 1972.

Art of the Airport Tower – Carolyn Russo. The airport tower as monumental abstraction.

Illustrations from Elektricität und Licht – Otto Lehmann [1895].

Incomprehensible Brainfuck talks formal L-Sys.

Commodore 8580 chip. Hi-res [133MB]. Plus many more at http://www.visual6502.org/ 

Ilya Prigogine on The Arrow of Time – Is time a fluid reversible cosmic commodity? – Omni Mag, 1983.

“The arrow of time is an arrow of increasing correlations.” Natalie Wolchover on entanglement as entropy.

Frolicsome Engines: The Long Prehistory of Artificial Intelligence – Jessica Riskin.

‘Others seek and achieve notoriety, Hinton has achieved almost total obscurity’ – Borges on Howard C Hinton and his Fourth Dimension.

Imaginary city landscapes by Georg Bohle.

the-trouvelot-astronomical-drawingsGroup of Sun Spots and Veiled Spots – E. L. Trouvelot [1873]

Theosophical images from Europe from the 1930’s at Lexicon magazine.

‘Some fractals were rejected by mathematicians and labelled pathological and monstrous.’ Infinite Space and Self-Similar Form – Laura Strudwick

Enlivening The Grid. On Channa Horwitz’s grid-system Sonakinatography.

Joe Banks, author of ‘Rorschach Audio’ on the visual construction of ‘reality’.

Chance and Order Group VII, Drawing 6 – Kenneth Martin. Lines between randomly defined points.

The strangely relaxing abstractions of Aeroese poetry – “Establish localiser two-seven-right”.

Geometric stimulation arrives from unlikely sources: 17C carpentry & joinery manuals.

Illustration from Man Visible & Invisible – Charles Leadbeater [1903].

Geodesic Model – William Donovan [1980] Made from ‘nit sticks’ used to check for head lice.

Théâtre Mobile – Pascal Häusermann.

One Response to “Selected Tweets #25: Sunspots, Fulgurites & Pathological Fractals”

  1. Radio Playlists writes:

    My favorite is Sydney Lévy’s book machinations part.

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Günter Haese – Antenna Wired for Air Vortex Transmissions

 Günter HaeseChronos – Günter Haese [2004]

In Günter Haese’s Chronos [2004] an array of radio antenna appear to be wired for aeolian transmissions. Carried to their receivers by micro bifurcating air vortexes the turbulent noise of air flow is the signal in this instance. In the cubic lattice of Kalogo [1999] an freeze frame animatronic of photons appear to be propagating through a crystal slowed down by a factor of a trillion seen through a compound eye. Yoshiwara II [1972] appears to be a point cloud materialized, but sagging under the weight of its own indifference to the environment and its audience.

German artist Günter Haese made a little over 400 hundred fragile mobile kinetic sculptures from brass wire, cogwheels, coils and clock springs in his lifetime. His wireframes of vibrating constellations and quivering parts were powered entirely by the flow of air. In Golf [1997] it’s clear to see the Paul Klee influences that Hasse was keen to mention in his work, but there are also strong hints of Duchamp enclosed inside this cubic trap.

 Günter HaeseGolf – Günter Haese [1997]

 Günter Haese Quirin – Günter Haese [2012]

 Günter HaeseResponsa – Günter Haese [1965]

 Günter Haese Janus – Günter Haese [1992]

 Günter HaeseKalogo – Günter Haese [1999]

 Günter HaesePinkus – Günter Haese [unknown]

 Günter HaesePokos – Günter Haese [unknown]

 Günter HaesePythagoras – Günter Haese [1997]

 Günter HaeseTransit – Günter Haese [1993]

 Günter HaeseYoshiwara II – Günter Haese [1992]

 Günter HaeseBaghdad – Günter Haese [1965]

One Response to “Günter Haese – Antenna Wired for Air Vortex Transmissions”

  1. paolo crosina writes:

    Dear Sirs,

    the Guenter Haese work titled Pinkus has been made in year 2007.

    Kind regards,

    Paolo Crosina

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Irvin Geis – Molecular Aesthetics as Network Idolatry

Irvin Gies Myoglobin [1961] – Irvin Gies

In Irvin Geis’s graphic molecule paintings the lightness of the wireframe structures perfectly counterpoints the cast iron logic of each molecules cryptographic configuration. Myoglobin, his most famous illustration published in Scientific America in 1961, took 6 months to complete. It’s frozen lattice of lushly hued paths abstractly coalesce into a connectionist idol; molecular aesthetics as network idolatry. Ribonuclease, with its graphic specular lighting and constructivist blue and red tones, presents molecules as scaled-up utopian architectural constructs rejecting the tyranny of utility.

 Lysozyme2 -  Irvin GiesLysozyme – Irvin Gies

 Lysozyme -  Irvin GiesLysozyme 2 – Irvin Gies

 Crambin -  Irvin GiesCrambin – Irvin Gies

Geis was trained as an architect. But the great depression of the ’30’s threw a curved career ball and he found himself working in the golden age of hand illustration for Fortune Magazine in 1930’s and then with Scientific America in the 1950’s. ‘According to Richard Dickerson, the UCLA biochemist who co-authored a number of major books on biochemistry, Gies’s genius wasn’t in depicting a protein exactly how it looked, but drawing it in a such a way that showed how the molecule worked, an artistic process that Geis called, ‘selective lying.’

Ribonuclease S -  Irvin GiesRibonuclease S – Irvin Gies

B-DNA -  Irvin GiesB-DNA – Irvin Gies

Cytochrome C -  Irvin GiesCytochrome C – Irvin Gies

Related:
‘It Must Give Off and Receive Light Like a Tiny Space Station’ – Kenneth Snelson’s Atoms

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Form Constants of Optical Mineralogy

form constants of optical mineralogyChromatic Polarisation of Light (German, unknown) [1895]

The Virtual Museum of the History of Mineralogy contains a large collection of scans from monographs on crystallography and mineralogy, arranged by author in alphabetical order, from 1450 to 1912. The chromolithographs of optical interference figures, mostly from the 19th century, record the passage of light through crystal lattices to reveal a corresponding geometric figure. Visualising the interference and chromatic polarisation of light during short mineral detours allowed mineralogists to decrypt the chemical constitution and locate the geological origin of each wafer-thin sample; photons moving at light speed were coaxed into perusing time-spans of billions of years. The proto-op art configuration of the figures echo the morphologies of Kluver’s Form Constants, Purkinje’s taxonomy of visual subjective phenomena and Chladni’s figures (which are, after all, also captive remnants of the properties of wave vibration). These intelligible ornaments deserve a place in collective unconscious for optical and spectral phenomena.

form constants of optical mineralogyPlate from Mineralogia Generale – Luigi Bombicci Porta [1889]

It was David Brewster, ‘the father of modern experimental optics’, who founded the sci­ence of optical mineralogy and first annotated these patterns. Knowing all too well of the allure of the prismatic figures he discovered during his polarisation experiments he invented the Kaleidoscope in 1816. This most famous of all optical toys encodes the laws and properties of light for amusement, as well the mechanics of symmetry and tessellation. Polariscopes and Conoscopes, the more serious utilitarian siblings of the Kaleidoscope, were the optical devices used to view and annotate the interference figures found in this post.

form constants of optical minerologyPlate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

form constants of optical minerologyplate from Mineralogie – Franz Wolfgang Ritter von Kobell [1864]

form constants of optical minerologyPlate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

form constants of optical minerologyPlate from Mineralogie – Gustav Adolf Kenngott [1890]

form constants of optical mineralogyOptical effects during the heat treatment of glass – David Brewster [1815]

form constants of optical mineralogyThe Phenomenon of Light (German, unknown) [1895]

Related posts:
Primal Generative: Form Constants & Entoptic Geometry
The Logic of Crystals – William T. Astbury & Kathleen Yardley’s Space-group Diagrams

2 Responses to “Form Constants of Optical Mineralogy”

  1. Whewell’s Gazette: Year 2, Vol: #03 | Whewell's Ghost writes:

    […] Data is Nature: From Constants of Optical Mineralogy […]

  2. Whewell’s Gazette: Year 3, Vol. #08 | Whewell's Ghost writes:

    […] Dataisnature: From Constants of Optical Mineralogy […]

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