© 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.