Archives for the Month of March, 2007

Robert Horvitz – Quantum Symmetries

Robert Horvitz
Page from my Diary – Robert Horvitz

Since the early 70’s Robert Horvitz has been making complex system drawings using a single mark repetitively. These marks, many thousands of them, are placed on the paper according to a predefined algorithmic process, the end result – symmetrical crystal patchworks and complex patterns plotting the imagined form of a quantum space-time.

More clues come from Horvitz himself:

’I was immersed in Pythagorean fantasy, reading up on natural proportions such as Planck’s constant, Hubble’s constant, the gravitational constant. I read an essay on Planck’s constant written by Erwin Schrodinger that was so brilliant and vivid in its description of the geometry of elemental matter that I am still immersed in the subject. But since the quantum concepts of physics came into my head months after I had reduced my drawing to combinations of a single element, I can’t say I do what I do because science says reality does it that way…”

Horvitz site contains many other fascinating annotations to his drawings taken from his journal as well as other writings for both Artforum and The Whole Earth Catalogue. That his work lead him to ruminate on geometry and topology come as no surprise:

‘Very quickly I saw that grids could be replaced by more general structures – arrays of cells, polygon tilings and froths. Spirals could be floppy, as in Form is the Language of Time. Geometry not only could be but, according to modern science, MUST be elastic, topological, based on similarities rather than equalities. This opened my mind to more dynamic forms: flows, decays, rips, shards, close-packings, eruptions, etc. These were more richly allegorical than the Euclidean motifs I had been using.’

Reese Inman – Algorithmic pointillist

Reese Inman
String Lattice – Reese Inman

Reese Inman uses computer algorithms to provide a map or blueprint for the construction of her paintings. Like a freeze frame from Conway’s Game of Life, and intricate mappings of other rare Cellular Automata, her paintings shimmer with pixillated light. From afar its is possible to imagine the final output has been made by a machine alone, but each individual element or pixel is hand painted providing a nice comment, as she mentions on her site, on the fragile imperfection of the repetitive human hand versus the endlessly robotic computations of the machine.

The works rely on a structure of individual units, bits of data, acting in unison to create an effect at a higher level. They make me think of Hofstadter’s chapter in GEB on ‘levels of description’ where he talks about ‘nearly decomposable systems’ where objects have a private identity but also contribute on a social level. In itself each pixel on a painting is just a flat colour, but looking at a painting as a whole, such as Matrix VI, we find effects of light, the movement pixels, and its hard not to imagine the next frames in an animated sequence.

Historically this work connects with the group of artists collectively known as the Algorists who used ‘detailed recipes for execution of an artwork’ and further back to Sol Lewitt’s instructional and rule-based modular art. There are also obvious ties to more recent Generative art as well as the Op Art movement of the 1960’s.

For more human computers see:

Procedural Drawings, Procedural Networks, Human Sorting Algorithm, Human Robots & Space Filling Emotions

Some geometric inspiration from India

yantra and rangoli
Sri Yantra

It’s nearing monsoon and Dataisnature returns to the seam after a few months in hibernation. Some inspirations from my travels in India.

The Yantra:

The Yantra is meditation diagram or ‘psychocosmogram’ containing linear and spatial geometrical permutations of the polarity between Shiva and Shakti. The form consists of the dot (or bindu – the mathematical point of zero dimension) and sets of mathematically defined interlocking triangles (upright for the male and inverted for the female) that are contained in a lotus circle as part of a larger diagram – the Mandala. ‘Yantra literally means loom, instrument or machine.

Yantras are found all over India, in temples and homes and within the contexts of worship and meditation. I was interested in the geometry of the Yantra, particularly the difficult to draw interlocking triangles, and wondered if there is prescribed way of making these symbols or a set of mathematical instructions?

What little info I could find mentioned instinctual methods of drawing these symbols, the result of practice and reference to a ‘mathematical’ meditation. A little browsing and I found this page, which gives very precise instructions, measurements and ratios for producing the sigil using a protractor, compass, pencil, and ruler. The page is also interesting in that it explains what some of the number ratios within the diagram represent in mythological terms.

Another page concerning the construction of the Sri Yantra, also containing pictures of beautiful three-dimensional yantras.
Images of Yantras

Added 27|03|07 : Mikel sent me a link to his research on the maths of the Sri Yantra plus other interesting findings.

Rangolis (also know as Kolams):

Rangolis, mentioned before at Dataisnature, are geometric drawings produced procedurally by joining up, or interweaving within, a skeletal matrix of dots (resembling a knitting pattern). These drawings are made by women early in the morning using chalk dust on wet earth. Hampi, built on the ruined city of Vijayanagar, seems to be the hotspot for seeing Rangolis in Southern India, not since the town awakes at 5am each morning – your early morning alarm call for a roam around the village to see these curious patterns being run in real time. Here’s a Flickr set containing my photographs of Rangolis in Hampi.

Rangolis are sign of invitation into the home, as well a symbol to prevent evil spirits from entering. They are also used to commemorate special occasions such as births or weddings, ‘When people get married, the ritual Kolam patterns created for the occasion can stretch all the way down the street. Patterns are often passed on generation to generation, mother to daughter.’ – wikipedia

Thanks to all those who sent mail while I was away, apologies if I could not reply while distant from wires (I’ll be processing them all shortly). And not so much thanks to the all the spam I received that made any response to comments on posts impossible. I had to go in and delete over 10,000 comments. Robots win! It’s likely that robots will take over the world in a more insidious way then previously imagined….

Anyway, comments are now switched back on and if you did post a comment in the last 4 months id be very grateful if you could do so again.