John A. Hiigli – Layering the Isotropic Vector Matrix

Cr_176_THREE_CUBE_OCTAHEDRONS_(FRONT) – John A. HiigliCr 176 Three Cube Octahedrons (Front) – John A. Hiigli

John A. Hiigli’s transparent pigment paintings and drawings combine aspects of transformation geometry, tessellation and subdivsioning systems. After discovering the work of Buckminster Fuller in the late 1960′s, and studying Fuller’s Geodesics and Synergetics, Hiigli has refined a body of work in which, typically, tetrahedral or polyhedral units are combined and layered to create dense lattices and translucent three-dimensional structures.

Cr_175_THREE_CUBE_OCTAHEDRONS_(side) – John A. HiigliCr 175 Three Cube Octahedrons (Side) – John A. Hiigli

Cr_194_CUBE_OCTAHEDRONS – John A. HiigliCr 194 Cube Octahedrons – John A. Hiigli

Many of Hiigli’s paintings model Buckminster Fuller’s Isotropic Vector Matrix – a skeletal framework and alternative to the standard xyz system, defined by cubic closest packed spheres, alternatively known as the face-centered cubic lattice to crystallographers. The spatial system of Isotropic Vector Matrix essentially translates to a geometry of least resistance.

CR56 – John A. HiigliCR56 – John A. Hiigli

CR50 – John A. HiigliCR50 – John A. Hiigli

CR143 – John A. HiigliCR143 – John A. Hiigli

‘When the centers of equiradius spheres in closest packing are joined by most economical lines, an isotropic vector matrix is disclosed. This matrix constitutes an array of equilateral triangles that corresponds with the comprehensive coordination of nature’s most economical, most comfortable, structural interrelationships. Remove the spheres and leave the vectors, and you have the octahedron-tetrahedron complex, the octet truss, the isotropic vector matrix’ – Buckminster Fuller.

VIRUS_XIX – John A. HiigliVirus XIX – John A. Hiigli

Cr_185_KALEIDOSCOPE – John A. HiigliCr 185 Kaleidoscope – John A. Hiigli

CR39 – John A. HiigliCR39 – John A. Hiigli

‘In complex constructions, increasing numbers of polyhedrons have a common nucleus embedded in a vector matrix. A large structure is embedded with a smaller structure, which encloses a smaller third structure, and so on. This decreasing volumetric relationship (‘change of scale’) of the structures produces the illusion of depth in space’ – John A. Hiigli

Related Post:
Drop City – Colonizing consciousness with abodes of Truncated Icosorhombic Dodecahedra

Further Readings:
Synergetics – Buckmister Fuller

One Response to “John A. Hiigli – Layering the Isotropic Vector Matrix”

  1. Charline Lancel writes:

    This image is vectorial or matrix, can it be both at the same time?

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Victory Over the Sun – El Lissitzky’s Drawings for Suprematist Automatons

Victory Over The Sun [Poster] - El LissitzkyVictory Over The Sun [Poster] – El Lissitzky

‘Every form is the frozen instantaneous picture of a process. Thus a work is a stopping-place on the road of becoming and not the fixed goal’ – El Lissitzky, Texts 1920-1923

El Lissitzky created his series of architectonic figures after seeing a production of Victory Over the Sun, the futuristic Russian opera with music by Mikhail Matyushin and costumes/stage designed by Kasimir Malevich. Premièred in St. Petersberg in 1913, the opera’s libretto was written by radical sound poet Aleksei Kruchenykh in the linguistically experimental and symbolic Zaum language. Paired up with Malevich’s set design and costumes, this pro-technological phonosemantic opera inspired Lissitzky to recreate figures of the opera’s main protagonists as suprematist automatons. A portfolio of ten large colour lithographs showing the main characters was published in Hanover in 1923. Lissitzky’s ultimate vision was to recast the opera as an electromechanical show with mechanical puppets. Much like his Proun (Project for the Affirmation of the New) series affirm the possibility of new utopian architectural forms, without explicit plans for their construction, his ‘Victory’ drawings imply the geometrical choreographies of constructivist automatons for the coming utopian machine age. The movements of figures are suggested by using shifting axes, multiple perspectives and directional signifiers. Lissitzky’s lyrical sense of humour is not withstanding whilst dealing with the tensions between pure abstraction, narration and representation.

New Man - El LissitzkyNew Man – El Lissitzky

The Announcer - El LissitzkyThe Announcer – El Lissitzky

Postman - El LissitzkyPostman – El Lissitzky

Anxious People - El LissitzkyAnxious People – El Lissitzky

Globetrotter (In-Time) - El LissitzkyGlobetrotter (In-Time) – El Lissitzky

Troublemaker - El LissitzkyTroublemaker – El Lissitzky

Old Man - El LissitzkyOld Man – El Lissitzky

Gravediggers - El LissitzkyGravediggers – El Lissitzky


The Architectural Fantasies of Iakov Chernikhov
Yuri Avvakumov – Agitarch Structures: Reconfiguring Utopia

Further Links:

Zaum and Sun: The ‘first Futurist opera’ revisited
The Historical Context of El Lissitzky – Dr. John Milner
El Lissitzky on Pinterest

One Response to “Victory Over the Sun – El Lissitzky’s Drawings for Suprematist Automatons”

  1. Dataisnature writes:


    Utopia LTD at GRAD in London presents an exhibition of Soviet avant-garde artwork reconstructed by Henry Milner. It includes works by El Lissitzky, Aleksandr Rodchenko, Vladimir Tatlin and Gustavs Klucis.

    There are 4 models of El Lissitzky’s ‘Victory’ figures:

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Paul Sharits: Declarative Mode [Against the Tyranny of Preconception]

Declarative Mode – Paul SharitsScore for Declarative Mode 6C – Paul Sharits

Paul Shartis’s scores for his film Declarative Mode, made in 1976-77, consist of coloured ink marks on graph paper, notating shifts between pure colour tones during frame transitions. Sequences of frame flicker, containing saturated hues, are reduced to tessellations of symmetry breaking motifs resembling fluid flow diagrams and lattice structures.

The film, itself, consists of two identical prints projected simultaneously, with one overlayed inside the other, and slightly out of sync, creating a non predictable and dynamic interplay between patterns. In this sense Sharits creates a bandwidth of partially deterministic possibility – there is some degree of randomness between predefined limits.

Declarative Mode – Paul SharitsScore for Declarative Mode 6B – Paul Sharits

Although known for his work as a structural film maker Sharits maintained that Declarative Mode was a ‘non-structural film and is narrative like, even while it contains much flicker. One cannot predict the scene by scene fabric, nor is there an overall unifying principle. The film attempts to be like-life full of unexpected twists and turns. It is an homage to Jefferson’s anti-slavery section of the Declaration of Independence and it is my declaration of independence from the tyranny of preconception, of working from an overall structure of structural logic’

Declarative Mode – Paul SharitsScore for Declarative Mode 3A – Paul Sharits

In Declarative Mode we see only a visual structure that gradually moves ‘from a measured poise towards an ecstatic level of colour-light pulsation (ending in micro-oscillations around 5 cycles per second, which is at the primary fade-wave cycle possible in sound speed 16mm film and is also a rhythm associated with certain neuron pulses during expansive, inspirational states of consciousness)’ – Paul Shartis in Stuart Leibman’s monograph [PDF]

Declarative Mode – Paul SharitsScore for Declarative Mode 3C – Paul Sharits

According to Anthony Bannon, ‘Sharits creates new hues not actually present upon the film through their co-temporal blending and through after-image retention. It’s a a complex phenomenon that yields sublime transitions across a spectral range, while the inner frame pulses with illusionistic movement as the hues change from warm to cool’

Declarative Mode – Paul SharitsUntitled, Undated – Paul Sharits [Colored drawing 60 x 60 x 40cm]

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Zimoun – 60 medical Infusion Sets, Water, Fire, Metal Sheets 20x20x4cm

This item was originally written for the printed issue of Neural Magazine – 45 Americas

Zimoun is known for his multiform artworks and installations created from commonplace industrial objects that explore array aesthetics combined with rhythmic sound. A recent work 60 Medical Infusion Sets, Water, Fire, Metal Sheets consists of a room containing medical drip sets each of which drops water onto heated metal sheets. On contact with the metal the water is instantaneously transformed into small jets of steam – moment of union being marked by a crisp hiss as water is vaporised by extreme heat. Over a period of time the metal sheets become oxidised and act as process canvases documenting the slow chemical transformation of metal into rust.

60 Medical Infusion Sets, Water, Fire, Metal Sheets 60 Medical Infusion Sets, Water, Fire, Metal Sheets – Zimoun

All dripping processes are emergent by virtue of the properties of fluid flow so that the rhythmic patterns of water dripping phase between randomness and order. Whereas the rhythmic sonic events in Zimoun’s previous works, such as 198 prepared dc-motors, wire isolated, cardboard boxes 30x30x8cm, were extremely dense, created by multiple non-synchronous sound-emitting motors, this recent work proposes a more meditative situation with respect to sound. Here, time is perceived to have slowed – the silent intervals act as strong counterpoints to the infrequent vaporisations. Each vaporisation draws our eye to its respective metal sheet generating a specific spatial awareness of the array within the installation.

98 prepared dc-motors, wire isolated, cardboard boxes 30x30x8cm 98 prepared dc-motors, wire isolated, cardboard boxes 30x30x8cm – Zimoun

Including elements such as water and fire in the title reinforces the alchemical intimations of the work. An extremely simple, taken-for-granted reaction, is represented as a primal elemental transmutation and recorded as irregular concentric oxide accretions. This piece, as with all of Zimoun’s work, relies on clinical aesthetics where multiple objects are spatially ordered while being precisely situated. These ‘architecturally-minded platforms of sound’ propose an array aesthetic that embraces­ minimalism and maximalism simultaneously.

Note: The term array aesthetic was originally proposed by Mitchell Whitelaw (You can read an interview Dataisnature made with him for Neural magazine here)

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Neri Oxman – Biomemetic Encapsulations of the Body

Pneuma 1 – Neri OxmanPneuma 1 – Neri Oxman

Neri Oxman, Assistant Professor of Media Arts and Sciences at the MIT Media Lab, is well known for her complex digital morphogenetic fabrications developed using biomimetic algorithms. In the past she has used the term ‘material ecology’, merging computation, biology and ecology, to describe her design process so that form-finding procedures are generated by throwing ‘environmental constraints into computational software’.

Pneuma 1 – Neri OxmanPneuma 1 – Neri Oxman

Pneuma 1 – Neri OxmanPneuma 2 – Neri Oxman

Pneuma 1 – Neri OxmanPneuma 2– Neri Oxman

Recent works such as the Pneuma series [2012], developed in collaboration with W. Craig Carter and Joe Hicklin, were modelled on the phylum Porifera. Corrugated and crenellated morphologies give rise to intensely coloured ‘architectural encapsulations for the human body’ [in relation to their environment based on protection, circulation and comfort].

Medusa – Neri OxmanMedusa – Neri Oxman

 Leviathan – Neri OxmanLeviathan – Neri Oxman

 Leviathan – Neri OxmanLeviathan – Neri Oxman

Stalasso – Neri OxmanStalasso – Neri Oxman

Nervous System – Colonies & Barnacles

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Prehistoric Messages of the Widmanstätten Cursive

Widmanstätten Pattern - Seymchan Meteor FragmentWidmanstätten Pattern – Seymchan Meteor Fragment

Widmanstätten Patterns, found in Octahedrite Iron meteorites appear in isometric configurations – their cursive lattice-work is reminiscent of the calligraphic paintings of both Mark Tobey and Brion Gysin. It was Austrian printer-scientist Alois von Beckh Widmanstätten who noted their patterns after removing rust from the Hraschina meteorite in 1808. This cryptic wildstyle of extraterrestrial origin was actually discovered 4 years earlier by an English Geologist G.Thomson, who treated the Krasnojarsk meteorite with nitric acid, similarly in order to clean it from rust. His claim to its discovery was obscured by, and lost in the ruins of the Napoleonic war.

Hraschina_HaidingerDrawing by M. W. Haidinger drawing depicts the fall of the Hraschina meteorite based on eyewitness accounts

In his book The Writing of Stones, Roger Caillois prompts us to read the inclusions and patterns of gemstones and minerals as if they were a secret cypher or as an aid to scrying. He asks us to delve into their unconscious symbolism in the same way Hermann Rorschach hoped to trigger psychological insinuations aided by the well-known symmetrical inkblots.

widmanstattenWidmanstätten Pattern

According to Marina Warner in her excellent essay, The Writing of Stones, material mystics such as Caillois ‘do not search for self-knowledge, nor for foreknowledge of their destiny or the sirens’ secret; but they emphatically investigate hidden meanings and scan the deepest horizons of time into infinity where the world turns into an inexhaustible book written in hieroglyphs’

What kind of messages might the Widmanstätten cursive encode? If Caillois was looking for the infinities of time contained in such hieroglyphs he would have come close to finding them here. Channelled through the language of exogeology we find that these scripts tell a very old story – as old as our solar system itself. The Widmanstätten figures of the Gibeon Meteor, which were formed in near zero-gravity conditions, are up to 4 billions years old. Here is a story of crystal patterns generated by an intergrowth of nickel-rich taenite and nickel-deprived kamacite during an extremely slow cooling process of one degree in every one thousand years. This means that were formed inside the dying core of a protoplanet.

gibeonSphereWidmanstätten Pattern at 40µm, 80µm, 400µm & 400µm [clockwise from top left]

The lithic meditations of the tribes of the Kalahari Desert, where the Gibeon Meteor impacted upon Earth in prehistoric times, may well have resulted in interpretations of a different kind. English Captain and Explorer Sir James E. Alexander, who was the first Westerner to discover the Gibeon, noted that these tribes used pieces of meteor to make tools and weapons. Most likely they may have also worshiped fragments of these fallen stones, as has been noted in many instances, making the Widmanstätten cursive the oldest sacred text in Solar System.

widmanstattenWidmanstätten Pattern

gibeonSphereWidmanstätten Pattern – Gibeon Sphere

Further Reading:

The Stone As A Witness Of Time in which Rohit Gupta explores the concentric geometry of Banded Agates as ‘encoding imprints of eclipses, occultations and syzygys’ and as the ‘etched memory of every single diurnal rotation of the planet on its solitary axis’. Furthermore his entire blog Compasswallah provides excellent reading.

The Writings of Stones – Images, annotations and quotes from Roger Caillois’s out-of-print book at 50watts.

The Worship of Meteorites – Hubert A. Newton

Related at Dataisnature:

The Lost Kingdoms and Scripts of the Lichens
Hypogean Wildstyle: Dominik Strzelec’s Byzantine Geology
Banded Agates, Sonic Hydrodynamics & the BZ Reaction
The Wave – Earth Waveform Oscillations

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Stanley Tigerman & G. T. Crabtree – The Formal Generators of Structure

The Formal Generators of Structure - Stanley Tigerman & G. T. CrabtreeThe Formal Generators of Structure – Stanley Tigerman & G. T. Crabtree

Architect Stanley Tigerman’s ‘The Formal Generators of Structure’ (Architecture & Urbanism Journal, 1975) explored the combinatorial use of rectilinear shapes to generate volumetric, optical and architectonic compositions. Spatial configurations of the square and cruciform are extruded to create axonometric projections reminiscent of the ‘ideal’ geometricism of the De Stijl school and the works of Op-artists such as Albers and Vasarely who toyed with the square to infinity through structural multiplicity and chromatic modulation. Tigermans paper published alongside his series of drawings (with G. T. Crabtree) explores many other examples of squared axonometry in art and architecture noting that:

‘Two rationalizations of the Western World have focused on the unchanging qualities of the right angle. One has been synthesized in art as a formal universality in the form of the square. The other has been synthesized in religion as a spiritual universality in the form of the cross’

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. Crabtree

The Formal Generators of Structure - Stanley Tigerman & G. T. CrabtreeThe Formal Generators of Structure – Stanley Tigerman & G. T. Crabtree

While pinpointing fundamental expressions of the square, historically, such as the Golden Rectangle and Le Modulor, Tigerman also looks forwards towards future computational strategies for composition.

‘As the world of art, as well as that of science comes to grips with ‘Systems Analysis’ and ‘The Field Theory’, it is necessary to formally analyze certain two dimensional, man-made diagrams to ascertain their fundamental characteristics to better under-stand the role they will play in the forthcoming computerized world of networks and lattices’

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Gravity is the Insidious Enemy of the Animate

Halo3 Screenshot - ThosHalo3 Screenshot – Thos

In 2007, gamer forum user Thos posted stills from a game of Halo 3 generated by a corrupt X-box. The sense of space and perspective is reconfigured through erroneous z-indexing and extreme texture scaling. Familiar buildings and vehicles are deconstructed to cubist extremities so that the rules of the game take on a more exploratory mode of interaction [also see previous post].

Halo3 Screenshot - ThorHalo3 Screenshot – Thos

drawing_woodsDrawing – Lebbeus Woods

These auto-destructive renderings of anomalous landscapes might by compared to the celebrated drawings of Lebbeus Woods. Woods’s broken and shattered façades, albeit elegantly composed, mock the Modernist ideal of an architectural utopia. His roboid skyscrapers half-eaten by parasitic substructures are viruses and program execution errors in the world of ‘established’ architecture.

Halo3 Screenshot - ThorHalo3 Screenshot – Thos

Sarajevo_Scar_woodsSarajevo Scar – Lebbeus Woods

Halo3 Screenshot - ThorHalo3 Screenshot – Thos

aero_livinglab_woodsAero Livinglab [detail] – Lebbeus Woods

The title of this post is a quote by Lebbeus Woods.

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Noctuelles – No Enemies, No Puzzles, No Obstacles

Tower - NoctuellesTower – Orihaus

‘Can we create a form of digital entertainment that explicitly rejects the structure of games? What is [the role of] an interactive work of art that does not rely on competition, goals, rewards, winning or losing?’ asks Michaël Samyn in the Notgames ‘Not a manifesto’.

Michaël’s call to action explores the possibility of the game-world experience as an artform, and as a platform for a creative [re]configuration of virtual space facilitating an exploratory experience of immediacy once the traditional ‘role’ is eradicated.

Tower - NoctuellesTower – Orihaus

Tower - NoctuellesTower – Orihaus

Structure Synth Test - Orihaus Structure Synth Test – Orihaus

Structure Synth Test - Noctuelles Structure Synth Test – Orihaus

Orihaus has create a series of ‘first person exploration’ games where there are ‘no enemies, no puzzles, no obstacles’ containing procedurally generated landscapes layered with constructivist megastructures. These environments provide the disembodied psycho-geographer with a possibility to inhabit purely abstract geometric topologies. Virtual derives can be acted out in collaboration with spatial connotations generated by memory and ‘real’ world associations.

Aeon - Noctuelles Aeon – Orihaus

Aeon - Noctuelles Aeon – Orihaus

Aeon - Noctuelles Aeon – Orihaus

Aeon - Noctuelles Aeon – Orihaus

Aeon - Noctuelles Aeon – Orihaus

Aeon - Noctuelles Aeon – Orihaus

Atelier - Noctuelles Atelier – Orihaus

Atelier - Noctuelles Atelier – Orihaus

Atelier - Noctuelles Atelier – Orihaus

It would do no harm to recall Debord’s call to action [from his Theory of the Derive]:

‘In a dérive one or more persons during a certain period drop their usual motives for movement and action and let themselves be drawn by the attractions of the terrain and the encounters they find there. The element of chance is less determinant than one might think: from the dérive point of view cities have a psychogeographical relief, with constant currents, fixed points and vortexes which strongly discourage entry into or exit from certain zones’

Structure Synth Test - Noctuelles Structure Synth Test – Orihaus

Structure Synth Test - Noctuelles Structure Synth Test – Orihaus

Structure Synth Test - Noctuelles Structure Synth Test – Orihaus

Lumiere, Orihaus’s most recent game used Structure Synth to generate all architectural forms and constructions within the environment [source here]. The grey sketches generated from its design grammar approach provide a strong counterpoint to the final game environments which use strong emotive glow, lighting and depth-of-field Shader effects.

Related Posts:

Mikael Hvidtfeldt Christensen – Structure Synth
Patabotany #2: Grow your own Worlds
The Endless Forest – Tale of Tales
Tohu777 – Structure Synth Architectonics

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Selected Tweets #19 – Dystopian Hyper-Fiction, Spaceplates & Bitrot Protected Visual Poetry

Ground Plan - Ned ScottGround Plan – Ned Scott

Selected tweets from my Twitter stream: MrPrudence with occasional annotation additions.

The War Rooms – Ned Scott. Hyper science-fictional dystopian drawings [after the Energy War of 2050].

Spaceplates – Anne Romme + N55′s customizable tessellated greenhouse system.

Susanne Kathlen Mader’s Geometrical Natures – abstract spaces & dimensions informed by de Stijl and Constructivism.

SpaceplatesSpaceplates – Anne Romme & N55

Susanne Kathlen MaderGeometrical Natures – Susanne Kathlen Mader

The Skor Codex Book [PDF]. La Société Anonyme’s encoded schematics and visual bitrot protected poetry:

‘The SKOR Codex is a printed book which was sent to different locations on earth in the year 2012 containing binary encoded image and sound files selected to portray the diversity of life and culture at the Foundation for Art and Public Domain (SKOR), and is intended for any intelligent terrestrial life form, or for future humans, who may find it. The files are protected from bitrot, software decay and hardware failure via a transformation from magnetic transitions on a disk to ink on paper, safe for centuries.’

SpaceplatesThe Fog – Espen Dietrichson

Espen Dietrichsons drawings combine analytical/geometrical elements to fragment images into abstract units.

Edo 6, Alhambra & Script – Toni Davey’s burnt/cut/lasered minimal geometric paper configurations.

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