For millenia, painting was representational to some degree. Although modern theorists like to talk in degrees of abstraction, the artist’s intent was to represent in paint some form of visual reality, whether tangible or imagined. The twentieth century brought paintings which didn’t set out to represent anything in particular, and ever since people have been claiming that their illustrious predecessors were somehow becoming more abstract.

In this and tomorrow’s article I’m going to consider one way of looking at this issue: emergence and scale. I will try to demonstrate that paintings can be read quite distinctly as representational or abstract, and that representational paintings can never tend to the abstract. The distinction is quite crisp.

The novel background to this comes in the strange forms seen in mathematical patterns such as the Mandelbrot Set, with which I am sure you are familiar, and fractals.

These composite views of the Mandelbrot Set start at the top left, and zoom in on its details according to the magnification shown. This fractal geometry shows a strange scaling effect: as you zoom in, you see details which closely resemble the outermost form of the Mandelbrot Set.

Although there are such fractal forms in nature – trees, branches, twigs, and leaves are commonly cited – in general nature scales very differently. There comes a point when minutiae like atoms and molecules undergo marked change in appearance, with the emergence of quite different organisational properties. We can see this in paintings.

This microscopic view of a cross-section of the paint layer of Honoré Daumier’s The Strongman (c 1865), made by conservator Elizabeth Steele in The Phillips Collection, shows the pigment particles which together form the colour which we perceive in an oil painting. Although they provide invaluable information about how the artist constructed that work, and can cast light on their painting methods, pentimenti, and much more, they tell us little of the painting’s intent or appearance.

We need to ‘zoom out’ further.

At this next level, very close up to John Constable’s early oil sketch on paper of Fen Lane, East Bergholt (c 1811), we can see the artist’s marks, their brushstrokes. The first inklings of structure and organisation are starting to emerge. Here we can guess that these are trees with foliage, but little more than that.

Zooming out further, more organisation appears, confirming that we are looking at trees and their foliage. But this is still a semi-chaotic tangle of brushstrokes.

When we look at the whole painting, its individual passages assemble into something which makes far greater sense: there is a man, striding down a lane in the Suffolk countryside, with glimpses of fields to either side of the avenue of trees.

What could easily have been mistaken for an abstract painting of more than a century later was, of course, something quite the opposite: a quick oil sketch made in front of the motif, with not even a smidgin of intent to ‘be abstract’, even if Constable had ever any conception as to what that might have meant.

My next example follows a similar course, starting in the weeds of detail in JMW Turner’s Wreckers – Coast of Northumberland, with a Steam-Boat Assisting a Ship off Shore (1833-4).

As you might expect from Turner, the finest detail shows a rich vocabulary of different types of mark. Some appear to have been made by a brush in a fairly conventional way, but others involve different tools, some perhaps the handle of a brush, or even his fingernails. The result is a primal chaos of vague colours without any real form.

Zooming out quite a bit, we can now see a distant cliffed coastline, a sailing ship with two masts, savage breakers (from which the first detail was taken), and people in the foreground.

Now we can read the painting much more clearly, with the steamship in the right distance, and the wreckers trying to salvage their treasure from the sea.

I admit to not being an expert on ‘abstract art’, but have drawn three examples for comparison from the media supporting Wikipedia’s main article on the subject.

The first is Natalia Goncharova’s Cats (rayist percep.[tion] in rose, black, and yellow) from 1913. There seems little point in looking at details of this painting, but with a title that suggests it might be representational, I don’t think this is a pure abstract by any means. I can see several black cats here.

Albert Swinden’s Untitled, from the his murals for the Williamsburg Housing Project in about 1939, seems a much stronger contender. It doesn’t have any title to suggest what I might envisage, and I can’t organise its colour fields into anything even vaguely representational.

We can perform the zoom test with Theo van Doesburg’s Composition XX from 1920. Above is its central four colour rectangles, and below is the whole painting. Although you can envisage patterns, this is pure abstraction: nothing organised into representation emerges here.

So my hypothesis is that all representational paintings appear chaotic, even abstract if you must, if you zoom in far enough. But as you zoom out you reach a point where their marks organise into an image which our brains see as representing the tangible or imagined. If you’re looking from afar at the whole painting and this fails to happen, then you can be confident that it is truly abstract art.

The unsolved mystery, which I will consider in more detail tomorrow as I look at a wider range of representational paintings, is how a painter working a few tens of centimetres from their paint surface can see the bigger picture, and organise their marks to become visually meaningful to the viewer.