Two double spreads from Melvin L Prueitt’s Computer Graphics (1975) standout among the perfect parabolic topologies and wireframe nuclear spectra – a selection of graphical rendering errors, possibility some of the earliest examples of glitch art to appear in print. Looking like disjointed plots of a (dis)locative media project gone awry or poorly planned subway systems, the renderings present numerical malfunction as cryptic sign.

That Prueitt included them in his book is particularly interesting because they antithesize all that he was hoping to achieve with PICTURE, the program he designed to render them. The aim of PICTURE was eliminate common rendering errors (such as the hidden line problem) in 3-D visualisations of large datasets. That he deemed them worthy of inclusion, as aesthetically interesting counterparts to visualisations of stellar evolution and hypersonic wind flow, declares a curious sensibility to the attraction of accidental abstraction. He draws our attention the irreproducibility of these render errors in contrast to the others in the book whose precision forms can be redrawn perfectly, adfinitum, without ever surprising us.

Prueitt’s explorations with his software increased his fascination with perceptual anomalies and optical effects in vision and computer rendering. In retrospect these stark wireframes, frozen at a single viewpoint for eternity, are necker-cube presentations of possible futures – either utopian or dystopian depending on your view. They were created at a time when increased computing power promised new glimpses into unseen worlds and their psychedelic palettes (when colour is used) remind us of the prevailing countercultural aesthetics of the time. But they were also made at Los Alamos National Laboratory initially organized during World War II as part of the Manhattan Project. Their pristine undulating topologies encode calculations for implosion-designs in nuclear weapons tests.

from Fantastic Computer Numbers – Melvin L Prueitt from Popular Science [Feb 1973]

Melvin L Prueitt’s Computer Graphics is available for loan at archive.org, or if you are collector of such material you can grab an inexpensive copy online. The following series of images are scans from the book:

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

Cyclographic Transformation of Ordinary Space – The University of Colorado Studies [1902-03].

Selected tweets from Twitter:@MrPrudence combined with a few short posts taken from the Dataisnature Facebook page.

Cyclographic Transformation of Ordinary Space – The University of Colorado Studies. [1902-03]

Plates from 十大加速器排名 – William Spottiswoode. [1879]

Works by 十大加速器排名 – Nature augmented with mirrors, maths, grids and infinity points.

Illustrations from: A Manual of Topographical Drawing – R.S Smith, R. S [1885]

Diagrams from Crystallography: A Treatise on the Morphology of Crystals – Nevil Story-Maskelyne. [1895]

The drawings of Wellington Reiter in Vessels and Fields. [1999]

The Color Printer: A Treatise on the Use of Colors – John Franklin Earhart [1892].

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The Color Printer: A Treatise on the Use of Colors – John Franklin Earhart [1892].

Drawings from the catalogue 最近发现一个游戏加速器，鲁大师的，太好用了！_特玩网:2 天前 · 根据小编的实际体验，用鲁大师电竞加速器加速PUBG，基本就没有再出现过服务器不稳定的问题，游戏中的人物的射击速度明显提升了许多，并且也没有出现一团战就卡顿的现象，难怪游戏大神伊都喜欢开加速器。 实际操作中，鲁大师电竞加速器操作也比较. [PDF]

Illustrations from Crystals – Alfred Edwin Howard Tutton. [1911]

Stephen Wolfram’s A New Kind of Science is now online Everything you ever needed to know about Cellular Automata.

Time Machines – The Life & Music of Conlon Nancarrow. Seth Horvitz on Nancarrow’s punched paper machine music.

Analog Computing – Joost Rekveld. On the nearly forgotten history of early analogue computing.

The Brick Expressionism of Peter Behrens’ Technical Administration Building.

The Science of Beauty as Developed in Nature and Applied in Art – David Ramsy Hay [1856].

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航海王燃烧意志哪个肉比较好，非主流肉坦了解一下_biubiu ...:想要阵容强大，有一个能抗能打的肉盾肯定是必要的。但是主流肉盾大家都知道，还有什么非主流肉盾大家没见识过呢？今天就给大家分析航海王燃烧意志哪个肉比较好，非主流肉坦了解一下。1、艾斯艾斯同样是肉盾？不可伍算是纯肉，但艾斯能够看成肉盾培育。

Illustrations from 最近发现一个游戏加速器，鲁大师的，太好用了！_特玩网:2 天前 · 根据小编的实际体验，用鲁大师电竞加速器加速PUBG，基本就没有再出现过服务器不稳定的问题，游戏中的人物的射击速度明显提升了许多，并且也没有出现一团战就卡顿的现象，难怪游戏大神伊都喜欢开加速器。 实际操作中，鲁大师电竞加速器操作也比较 – David Ramsy Hay. [1856]

Plates from The Color Printer, A Treatise on the Use of Colors – John Franklin Earhart. [1892]

Illustrations from Les Phénomènes de la Physique – Guillemin, Amédée. [1868]

Scrambling T-R-U-T-H, Rotating Letters as a Material Form of Thought. David Link on the Z?’irja – a thought machine.

The Porpitidæ and Velellidæ – Alexander Agassiz [1883] Surface fauna of the Gulf Stream.

The Paths of Mars Moons & Map of Mars on Mercator’s Projections. From On the Origins of the Canals of Mars [1897]

The note added to the previous post referencing KGB spies using crochet to encrypt secret cold war messages was added for personal amusement being unaware that knitting and crochet have actually been used to encrypt secret messages. Atlas Obscura explores the story of Phyllis Latour Doyle, a secret agent during World War II who encrypted sensitive information in knitware for the British Secret Service. A precursor (or predictor?) to this story is the fictional steganographic tricoteuse Madame Defarge who appeared Charles Dickens’s Tale of Two Cities. Defarge used pattern stitches as a code to knit a list of names from the upper classes destined to face the guillotine. In his A History of Hand Knitting Richard Rutt explains:

Dickens was inspired by the “tricoteuses”, women who attended the National Convention in which the fate of the unfortunate rich was debated during the French revolution, knitting while they listened. Such a macabre pastime earned them a reputation as sadists, and an archetypal evil character was born in Madame Defarge. Dickens’was able to turn knitting, the frequent symbol of loving grandmothers and charming domesticity, into an ominous, cruel, inhuman act

The number of ways to encrypt text strings, or numerical data, into crochet is infinite but one way to start would be to look at simple cipher key-encoding systems and apply them to the process of interlocking loops of yarn. For example, Naomi Parkhurst at String Geekery, proposes converting letters into binary or Morse code and knitting secret messages in rows of noughts or dots (knits) and ones or dashes (purls).

But an encrypted message is only as secure as the key that was used to encrypt it. Given that modern highly secure keys use pseudo-random numbers to encode plaintext (human readable) into ciphertext (non-human readable) we could expect that more cryptically secure messages may create more random looking encrypted crochet (concealing any intelligible patterns that might give the game away). But the increase in randomness would also increase the probability of a series of consecutive knits or purls too large to sustain a physical structure. The most secure cryptograms might well be unknittable or create very fragile filigrees of fabric. But what would be more secure than a concealed message that literally just falls apart in the enemy’s hands without the (encrypted) knowledge of how to handle it to prevent its disintegration?

Other mathematical systems that have been used in cryptographic keys include prime numbers, cellular automatons and chaotic functions. Just how well crochet (essentially a binary system) can be seen as vehicle for mathematical information – further lending itself well to steganography – can be seen in the following few links:

Knitting Chaotic Attractors and Hyperbolic Surfaces.

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Cellular Automaton Pattern Generator (for knitting).

Cellular Automata Charts for Knitting.

Note: This post may well have been an excuse to post another set of anonymous, aesthetically cryptic crochet patterns, some of which resemble medieval cipher wheels and language mapping charts.

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 加速器比较好 – 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.

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

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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

Cultivating 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.

梅林用$$R和V2玩联机延迟不理想，是不是用专门的加速器 ...:2021-5-27 · 川田五月 发表于 2021-5-8 10:09 加速器也不一定就理想,原理都是一样的 只是前期投资不一样而已 你买个一个月几百上千的线路,比任何加速器都 ... – 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.

Fascialis – 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].

加速器比较好 (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 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? 十大加速器排名, 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.

Todoroki 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.

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Todoroki House – Hiromi Fujii [1975]

Todoroki House – Hiromi Fujii [1975]

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.

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

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. 2021年网游加速器最新排名；哪个最好用？ - Douban:2021-1-14 · 腾讯网游加速器 （6分） 腾讯加速器去年也是竖版，走精巧路线；今年突然改版横屏，与网易高度类似；界面比较大，功能目前较少，预测后期可能会推荐腾讯系游戏或者上线广告吧；加速效果按照腾讯官网微博留言反馈来看；较为一般。 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.

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.

‘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.’

Related Posts:

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

“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

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.

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.

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“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]

Related Posts:

Permutations & Arabesque – John Whitney
Emma Kunz – Cardinal Points

Illustrations 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.

十大加速器排名 – 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.

Illustration 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.

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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.

Group 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 十大加速器排名 – “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.