Geometric Abstraction

From Mondrian to Pollock, by way of Matisse.

[see also my more recent post of March 2014]

When we conventionally use the term Geometric Abstraction in art, we tend to be referring to works by artists like Piet Mondrian, such as his Composition series.

Piet Mondrian

The generic aspect of these Mondrian images, apart from that they are abstract in the sense of being non-representative or non-figurative, is that there are clear elements of geometry in the major components. In Mondrian's case,  these elements are rectangles and straight lines. This is a very narrow use of the concepts of geometry. Even when we include triangles and circles as other artists do we are still taking the term geometry in its narrowest sense.


The Mondrian is typical of many of his late paintings, where the color fields are rectangular, the palette is restricted and the elements are separated by strong black vertical and horizontal lines

Other artists whose work falls into this very tight classification of Geometric Abstraction include Frank Stella, Ben Nicholson and Bridget Riley.

Frank Stella

The Stella shown here is also typical of a whole series of paintings that he has done on the theme of nested squares. Often these images appear in related pairs. This is just a single image.

Stella's geometry is more subtle than a casual glance at the image might imply. The colors are in a carefully chosen order that he often repeats in other paintings.

Alternate squares coming in from the edge are greys, shifting evenly from black to white. The intermediate squares are colors from a color-wheel or spectral order used repeatedly by Stella (YORGBV). In this image (Gray Scramble) the squares are painted in such a way that a tiny band of naked canvas shows between each one (about 5mm on a 1m canvas, I recall).

Ben Nicholson

The Nicholson is again one of a series of images, produced over a few years, in which rectilinear shapes are superimposed, with the occasional circle or shadow to take the eye's attention. In this example, the shapes are simpler than a casual glance might suggest. The black element is a square that has been (logically, if not physically) overpainted by a white rectangle that in turn has been overpainted by a red square. Or alternatively these shapes could be described as a consequence of intersecting stencils. In practice, if I recall correctly, the original is painted directly onto a pencilled drawing.

Bridget Riley

Finally, in these few examples is a simple Bridget Riley; simple compared with some of her monumental geometric constructions.

Again, this example is one of a family of similar images (paintings and prints, I think). The geometry here is the regular arrangement of a repeated shape on a grid. The shape here is a small black elliptical lozenge. At each point on the grid the orientation of the lozenge is varied. The variation is uniform. The repeated pattern is that the lozenge is recorded in eight gently rotating positions, before the pattern repeats itself. This pattern-of-eight itself repeats, shifted one grid place, to give an overall optical-illusion-effect of two rolls meshing together. Riley did many variations of this idea, large and small, with colors reversed and sometimes adding another optical effect that typifies some of her images, of slowly changing the shade of the repeated element to create a misty appearance (not shown here).

I mention these examples because it is obvious in each one where geometry plays a significant role and why we might classify them as Geometric Abstraction. I want to suggest a slightly broader interpretation of the use of the term Geometric in the classification of images such as these. I want to argue that the geometry isn't just to do with shapes and layout but also to do with color and process and impression.

The most obvious use of geometry in painting is the centuries-long effort to perfect perspective in figurative and representational images. This geometric problem of creating the illusion of accurate depth on a flat canvas was solved by deriving geometric rules from a mathematical understanding of optics, rules such as vanishing points.

Photographs, using a standard lens, construct that illusion exactly on the print, as artists had for centuries worked to perfect. Despite this manifest geometrical relationship between the scene and the image (made manifest by the optics), we wouldn't want to us the term geometrical to describe such an image.

Yet, where in painting, false-perspective is created, we might venture to call the work geometric. Where the idea that the artist is promoting is established by exaggerated or skewed perspective, we might venture to use the term geometric to describe that work. This abstraction from reality that is achieved through false perspective is right at the boundary between abstraction and representation. It is an area that I find fascinating. It is something I will return to later.

In abstract works that are apparently random, or arbitrary, in their use and layout of shapes, by artists such as Pollock, Miro and Matisse, I could also argue that the creation is essentially geometric, and that that term could be used to describe them.

Take for example, Matisse's cutouts. The shapes may seem arbitrary. They were apparently cut with scissors by the artist (lying on his back, ill in bed) and are typically 30 to 40 cm across (I recall). The scissors have typically followed a continuous, smooth in-and-out path to complete a closed curve.

cut-outs, based on simple geometric descriptions

Geometers will recognise the use of the terms continuous, smooth and closed in that sentence and could reproduce Matisse-like cutouts with just a couple of equations, as I have done here.

Pollock is a harder case to argue. He is often held out as the opposite of geometric, in that his action paintings from late in his career, having been created by pouring and splashing paint on a horizontal canvas, have no aspect of geometry about them. This is true in the traditional sense of geometric, where this term is used to conjure up the idea of squares, triangles, lines and regular curves.

But if we were to contemplate how we might reconstruct a Pollock, we would plan our pouring and splashing in a systematic fashion that would have significant elements of geometry about it.

A splash for example is an elongated smooth continuous closed curve (filled with paint). We could describe that geometrically, as we have done for Matisse's cut-outs.

Poured shapes are similar, fatter. The arrangement of shapes in a Pollock is random ... ish. They are separated by regular(ish) distances. They are arranged (in layers) to cover the canvas until the ratio of overpainting to underpainting satisfies the artist. That ratio can be described geometrically too.

It may be that we should prefer to describe Pollock as a Systems artist where his process is the systematic component, rather than his geometry. I see this distinction as being just different facets of the same coin. This is something I need to expand on later. [eventually, in December, I did create an image after Pollock]

Somewhere between the extremes of Mondrian and Pollock on the spectrum of geometric abstraction we find artists like Miro and O'Keeffe. Miro can be seen as somewhere between Matisse and Pollock, perhaps nearer to Matisse.

O'Keefe on the other hand looks like she favoured figurative or representational subjects for her paintings. The most familiar are the flower-heads that many take to be reminiscent of abstract genitalia. As likely an explanation is that they are abstract geometric shapes which, in a manner similar to cubism, are supposed to give the impression of a subject rather than an accurate representation.

after O'Keeffe

When you look at O'Keeffe's landscapes and cityscapes you can see a similar simplification towards favouring the geometric over the realistic.

This tendency towards geometric abstraction from the modern artists of the early twentieth century is interesting, particularly in the context of the advent of photography and the movement of photography from the journalistic to the artistic, about which O'Keeffe must have known a great deal.

It is tempting to extend the term geometric abstraction to embrace these extremes. To include O'Keeffe and Pollock.

Since my objective is to seek out the systematic in modern and contemporary art, and since geometry is perhaps the simplest manifestation of the systematic, I will tend to use the term geometric when discussing the works of artists such as those discussed here. 

In a similar vein, photography moved from the figurative to the abstract by emphasising the geometric. Witness the many photographs of landscapes and cityscapes that are manipulated (in terms of cropping and exposure etc.) to emphasise color and shape over the detail that a scientific or journalistic photograph might choose.

Abstract photography finds geometry (in its wider sense) in the natural or built world.

However, when photography is simply a component in an otherwise more elaborate abstract work, such as a Warhol or Richter, how should be categorise that?

I have chosen to use the term Photographic Abstraction (in homage to geometric abstraction) and will, in what is to follow, try to justify that choice by linking the concepts of systems art, geometry, photography and abstraction. More on that in due course.