26 March 2011


Equinox, paper collage on hardboard, 91cm x 130cm
© 2010-2011 w roberts

In 2003 I painted two separate 'VP's (see below post, Varignon Parallelograms) on unframed irregularly-shaped quadrilateral canvases. More recently I had the idea of composing a picture consisting of many interconnected and interrelated Varignon Parallelograms. That's what you see here. There was infinite scope to intuitively feel my way through this composition, it's just that I stuck to this particular theorem in this piece as an underlying unifying principle. It's really no different in essence than painting a picture and restricting yourself to (say) just three colours. It's simply a principle that adds another form of coherence or unity to a work. And it's kind of interesting when you paint something like this (Equinox above) and you're actually conscious of this 'qualifying principle' or 'syntactical rule' that helps strike a different kind of balance or interchange between regularity and irregularity.

The main additional qualifying geometric syntactical rule I set for myself was that each side of an irregular quadrilateral in the work would be exactly the same length as, and gaplessly adjacent to, its neighbouring irregular quadrilateral on that edge. This means that the work became, by definition, a form of 'tessellation of the plane' (i.e. 'tiling pattern') but one that's quite unusual in that it's both 'demiregular' and aperiodic. That is, half its area is 'half-regular' (contains interconnecting unique parallelograms that are joined at their vertices), and it is aperiodic because there are no repeating (i.e. periodic) sequences or patterns that recur at identical or cyclically spaced intervals. It is equally regular and irregular.

Other secondary principles include: the four triangles that surround any given Varignon parallelogram (and so defining its encompassing irregular quadrilateral) were to be of free intuitive colour choice, yet once chosen, had to be the same (which you can see). The total number of colours was restricted to mainly 8 (relating to the number of notes in an octave or scale, with 1 or 2 additional very closely related 'enharmonic' colours (near not only in chroma but close also in value or tone). In this way I tried to bring a music scale or 'key signature' concept to the work. Brighter colours and/or those of stronger tone or value I generally restricted to the smaller shapes.

This work was virtually complete approx 6 months ago but for various reasons couldn't get it posted til now.
 [I've been offline for quite a while due to extenuating circumstances. Am hoping to now get around to answer emails, blog rounds of friends, asap. So please bear with me, there's some catching up to do here! If you've had any bounced emails, i changed my ISP last year so that's likely to be the reason why, and so I may never have actually seen those. Apologies in advance if that's been so.]

The beginning was fully free. And even once started, many of the quadrilateral corners could be placed anywhere, fully intuitively. But others were necessarily shared, and therefore fixed into position by a previously placed corner/vertex.

A simple visual poem or metaphor of Universal instantaneous non-local interconnectedness?? Imagine moving a node-point or vertex 'locally' within the composition. Then think about how other node points and quadrilaterals would have to change in order to accommodate that single change remembering that all shapes, and at all times, must follow the same syntax rules governing their interdependency. The effect would be a simultaneous reconfiguration (movement to new positions) of all node-points, and therefore of necessity all quadrilaterals, in short, of everything else at any distance, even for all forms which follow the same syntax, and which may extend outside the painting's boundary, to infinity. In other words the configurations could be interpreted as a 'captured instant' of a dynamic and infinite interconnectedness. You can imagine any node (vertex) in this 'interconnected form-field', that if it moves at all, then the whole field is of necessity instantaneously reconfigured and must also therefore move. In this respect the painting points to an interdependency and interconnectedness of form and motion.

(c) copyright 2006 w roberts

This idea of dynamically interconnected forms, and of their ubiquity in Nature, clearly resounds within this small photo (above), looking down towards my feet, of a thin wave that was rippling up the mirror-perfect reflective beach sands, where land meets sea.


Nick said...

A fascinating piece and most enlightening explanation (I actually "get" it, at least to a point). I can imagine that if the whole thing were somehow hinged/adjustable, moving one of the nodes/intersections would create a new composition, though adhering to the same principles with the adjacent equal sides. I'm really taken with this piece, and wonder if the order and logic behind it is why, rather than just a random approach. And of course working within color parameters that represent the musical scale. When you mention octave, are you referring to the seven different notes within the octave, or actually encompassing the span of an octave and, in turn, representing the higher tonic differently. Enharmonic colors! There's another concept to stretch my meager brain. I'm sure I told you that long ago the idea of forming a unifying theory that fuses visual and sonic art was something that I surmised could be done. And since those are my main two interests in life, you'd think I might have made some plodding headway along those lines. Nope! This work is for a man versed in not only the arts, but the hard sciences.
Good to see you back online Wayne! :)

wayne said...

Hi Nick, thanks for your time and for your kind and interesting insights and observations, and, for what is clearly (to anyone who knows you) an incredibly self-effacing comment, from you: a recognized master in both the visual arts and music, having won accolades in both these arenas!
Yes I've been out of web/blog circulation for quite a while).
Regarding the piece and your observations/questions, I had similar questions from the outset in this in that it's an experimental piece ('logic' vis a vis 'randomness', or rather these opposites actually intertwined and interdependent).
Re the 'music scale' idea, that was consciously if somewhat loosely connected to my working through the piece. The '7 notes' connection -- you've got it. As for the 8th being the higher tonic, I thought about that (for example) a high-key red versus a low-key red with 7 intervening value/tone steps, but decided against a literal or transliteral application here in this piece, although that could be an interesting varied angle, especially maybe in a larger more complex work with huge numbers of spaces, and thus allowing for similar 'resonances' of shapes/proportions (octaves, etc). But in this comp which contains a smaller number of shapes I chose colors (including values/tones) as though they have the 'character' or feel of the intervals of a musical scale. These color choices were purely intuitive and not based on any 'math' (some will be pleased to know! :P ).
Re the enharmonic, =maybe a too fancy or 'out-of-circulation' word, used here to indicate a note/color that is common within or between two color-scales/keys, a color that 'links or is common to both. For example there's a chocolate-brown quadrilateral near the middle, (milk choc heheh): chosen as a color that's unique within the comp yet hopefully subtly connected to (harmonious within) the color-scale of the painting. This color could potentially form a 'bridge/link' (musically speaking) to another 'nearby' but different color-scale (here, out-of-view),, much like modulating to a different key yet 'logically connected to' (and 'sounding naturally to follow from') the former. Considered that way the work could be interpreted as a window on a much larger field, but of an infinite variety of 'color scales' (kind of 'rippling')..
The idea of a field out-of-view but logically connected to 'what is being observed now' (i.e. the comp 'window') parallels the way we 'take in' (listen to) the whole of a musical composition: a 'moving moment', the 'now-wave' that carries the listener beyond the present notes and chords of the moment to journey through themes, rhythmic variations, to a conclusion which although usually asymmetric is no less *whole*. Hope that makes some sense to someone :P ..
cheers and thanks again Nick!

Nick said...

I'm thinking....

W. K. Moore said...

Hi Wayne - I approach this work as I would approach Broadway Boogie Woogie. Let the eyes and mind to the work and bypass the analytical. However, I do enjoy your explanation of the work's construction and it is important of course otherwise there'd be no piece. That the visual undulates, breathes and fascinates is a testimony to the idea behind it. It's a groove to hang out with this and let it do its magic.

wayne said...

Nick, .. you've brought to mind a certain silent powerful 'posture of immortalized thought' rendered by one A Rodin.. All I can do is wait and wonder..for new angles, perspectives, insights..and for the fleshing out of thoughts whether in words, art, music.. ..Many thanks again Nick for sticking around and thinking on this one..

Hi Bill, ..it's always an honor to receive your feedback and glad you like the 'groove' here. That you picked up on the Boogie Woogie vibe/connection is a curious synchro, spot on, since although it wasn't mentioned in the notes to the painting, the work pays homage to Mondrian's famous pioneering abstract 'Square' compositions and his NY Boogie Woogie abstracts (to which you allude/refer).
Bill, that you've drawn a parallel between this and the Boogie Woogie, even if the lines here don't meet at the horizon, puts a smile on the inside..
Thanks again and cheers, wayne

Nick said...

How cool to see two of my favorite people in the same thread! Two guys way ahead of the curve.
Well, you've played an instrumental part in awakening in me an interest in science - cosmology, physics, biology. Unfortunately my mathematical prowess never made it past simple geometry, so the lectures I'm listening to on youtube by Larry Krauss, Weinberg, Coyne, and several others are probably not appreciated as fully as they should be. Though it's my understanding that nobody really gets quantum mechanics, not even the Feynmanns. I owe much of this to our discussions and correspondence, and Richard Dawkins. Krauss has blown my mind talking about the universe being flat, and energy coming from nothing. Mind blowing! Too late for me to explore science the way I would have liked, but maybe there is a link with the artistic temperament, yes?