Tomorrow a new exhibition by Peter Randall-Page opens at Pangolin London, called Upside Down & Inside Out. Peter has a long-standing interest in natural processes responsible for the appearance of pattern and form, inspired by the ideas of D’Arcy Thompson. It has been my privilege to write an essay for the catalogue of this exhibition, which is freely available online. Here’s the piece anyway.
There are, in the crudest of terms, two approaches to understanding the world. Some seek to uncover general, universal principles behind the bewildering accumulation of particulars; others find more enlightenment in life’s variety than in the simplifying approximations demanded in a quest for unity. The former are Platonists, and in science they tend to be found in greater numbers among physicists. The latter are Aristotelians, and they are best represented in biology. The Platonists follow the tree to its trunk, the Aristotelians work in the other direction, towards branch and leaf.
The work of artist and sculptor Peter Randall-Page explores these opposing – or perhaps one should say complementary – tendencies. He sees them in terms of the musical notion of theme and variation: a single Platonic theme can give rise to countless Aristotelian variations. The theme alone risks being static, even monotonous; a little disorder, a dash of unpredictability, generates enriching diversity, but that random noise must be kept under control if the result is not to become incomprehensible chaos. It is perhaps precisely because this tension obtains in evolution, in music and language, in much of our experience of life and world, that its expression in art has the potential to elicit emotion and identification from abstract forms. This balance of order and chaos is one that we recognize instinctively.
This is why Peter’s works commonly come as a series: they are multiple expressions of a single underlying idea, and only when viewed together do they give us a sense both of the fundamental generating principle and its fecund creative potential. The diversity depends on chance, on happy accidents or unplanned contingencies that allow the generative laws to unfold across rock or paper in ways quite unforeseen and unforeseeable. Like Paul Klee, Peter takes lines for a walk – but they are never random walks, there are rules that they must respect. And as with Klee, this apparent constraint is ultimately liberating to the imagination: given the safety net of the basic principles, the artist’s mind is free to play.
It might seem odd to talk about creativity in what is essentially an algorithmic process, an unfolding of laws. But it is hard to think of a better or more appropriate term to describe the “endless forms most beautiful” that we find in nature, and not just in animate nature. We could hardly fail to marvel at the inventiveness of a mind that could conceive of the countless variations on a theme that we observe in snowflakes, and it seems unfair to deny nature here inventiveness merely because we can see no need to attribute to her a mind, just as Alan Turing insisted that we have no grounds for denying a machine “intelligence” if we cannot distinguish its responses from those of a human.
This emergence of variety from simplicity is an old notion. “Nature”, wrote Ralph Waldo Emerson, “is an endless combination and repetition of a very few laws. She hums the old well-known air through innumerable variations.” When Emerson attested that such “sublime laws play indifferently through atoms and galaxies”, it is surely the word “play” that speaks loudest: there is a gaiety and spontaneity here that seems far removed from the mechanical determinism of which physics is sometimes accused. For Charles Darwin, one can’t help feel that the Aristotelian diversity of nature – in barnacles, earthworms and orchids – held at least as much attraction as the Platonic principle of natural selection.
But one of Peter’s most inspirational figures was skeptical of an all-embracing Darwinism as the weaver of nature’s threads. The Scottish zoologist D’Arcy Thompson felt that natural selection was all too readily advanced as the agency of every wrinkle and rhythm of organic nature. The biologists of his time tended to claim that all shape, form and regularity was the way it was because of adaptation. If biology has a more nuanced view today, Thompson must take some of the credit. He argued that it was often physical and mechanical principles that governed nature’s forms and patterns, not some infinitely malleable Darwinian force. Yet at root, Thompson’s picture – presented in his encyclopaedic 1917 book On Growth and Form – was not so different from Darwin’s insofar as it posited some quite general principles that could give rise to a vast gallery of variations. Thompson simply said that those principles need not be Darwinian or selective, but could apply both to the living and the inorganic worlds. In this view, it should be no coincidence that the branching shapes of river networks resemble those of blood vessels or lung passages, or that a potato resembles a pebble, or that the filigree skeletal shell of a radiolarian echoes the junctions of soap films in a foam. Thompson was a pioneer of the field loosely termed morphogenesis: the formation of shape. In particular, he established the idea that the appearance of pattern and regularity in nature may be a spontaneous affair, arising from the interplay of conflicting tendencies. No genes specify where a zebra’s stripes are to go: if anything is genetically encoded, it is merely the biochemical machinery for covering an arbitrary form with stripes.
The exoskeleton of a radiolarian
It is a fascination with these ideas that gives nearly all of Peter’s works their characteristic and compelling feature: you can’t quite decide whether the impetus for these complex but curiously geometric forms came from biology or from elsewhere, from cracks and crystals and splashes. That ambiguity fixes the imagination, inviting us to decode the riddle. This dance between geometry and organism is immediately apparent in the monumental sculpture Seed commissioned by the Eden Project in Cornwall: an egg-shaped block of granite 13 feet high and weighing 70 tonnes, the surface of which is covered in bumps that you quickly discern to be as apparently orderly as atoms packed together in a crystal. But are they? These bumps adapt their size to the curvature of the surface, and you soon notice that they progress around the ovoid in spirals, recalling the arrangements of leaflets on a pine-cone or florets on a sunflower head. Can living nature really be so geometric? Certainly it can, for both of those plant structures, like the compartments on a pineapple, obey mathematical laws that have puzzled botanists (including Darwin) for centuries. These plant patterns are called phyllotaxis, and the reason for them is still being debated. Some argue that they are ordered by the constraints on the buckling and wrinkling of new stem tissue, others that there is a biochemical process – not unlike that responsible for the zebra’s stripes and the leopard’s spots – that generates order among the successively sprouting buds.
Seed, by Peter Randall-Page, at the Eden Project, Cornwall, and the inspiration provided by pine cones.
The bulbous, raspberry-like surface of Seed was carved out of the pristine rock. But in nature such structures are typically grown from the inside outwards, the cells and compartments budding and swelling under the expansive pressures of biological proliferation. “Everything is what it is”, D’Arcy Thompson wrote, “because it got that way” – a seemingly obvious statement, but one that brings the focus to how it got that way: to the process of growth that created it. With this in mind, the bronze casts that Peter has created for this exhibition are also made “from the inside”. They are cast from natural boulders shaped by erosion, but Peter has worked the inner surfaces of the moulds using a special tool to scoop out hemispherical impressions packed like the cells of a honeycomb, so that the shapes cast from them follow the basic contours of the boulders while acquiring these new frogspawn-like cellular patterns on their surface. By subtracting material from the mould, the cast object is itself “grown”, emerging transformed and hitherto unseen from its chrysalis.
A new work by Peter Randall-Page (on the right) being cast at the foundry.
The organic and unfolding character of Peter’s work is nowhere more evident than in his “drawings” of branching, tree-like networks: Blood Tree, Sap River and Source Seed. These are made by allowing ink or wet pigment to flow under gravity across the paper in a quasi-controlled manner, so that not only does the flow generate repeated bifurcations but the branches acquire perfect mirror symmetry by folding the absorbent paper, just like the bilateral symmetry of the human body. The results are ordered, but punctuated and decorated with unique accidents. The final images are inverted so that the rivulets seem to stream upwards in increasingly fine filaments, defying gravity: a process of division without end, arbitrarily truncated and all emanating from a single seed. The inversion suggests growth and vitality, a reaching towards the infinite, although of course in real plants we know that these branches are echoed downwards in the traceries of the roots. There is irony too in the fact that, while sap does indeed rise from trunk to tip, driven by the evaporation of water from the leaf, water in a river network flows the other way, being gathered into the tributaries and converging into the central channel. Nature indeed makes varied use of these branching networks – and often for the same reason, that they are particular efficient at distributing fluid and dissipating the energy of flow. But we must be vigilant in making distinctions as well as analogies in how they are used.
Peter Randall-Page, Blood Tree and Sap River V.
Were real trees ever quite so regular, however? Some of these look more like genealogies, a mathematically precise doubling of branch density by bifurcation in each generation – until, perhaps, the individual branches blur into a continuum. We could almost be looking at a circuit diagram or technical chart – and yet the splodgy irregularities of the channels warn us that there is still something unpredictable here, as though these are computer networks grown from bacteria (as indeed some researchers are attempting to do). If there can be said to be beauty in the images, it depends on this uncertainty: as Ernst Gombrich put it, the aesthetic sense is awakened by “a struggle between two opponents of equal power, the formless chaos, on which we impose our ideas, and the all-too-formed monotony, which we brighten up by new accents”.
The vision of the world offered by Peter Randall-Page is therefore neither Platonic nor Aristotelian. We might better describe it as Neoplatonic: as asserting analogies and correspondences between apparently unrelated things. This tendency, which thrived in the Renaissance and can be discerned in the parallels that Leonardo da Vinci drew between the circulation of blood and of natural waters in rivers, later came to seem disreputable: like so much of the occult philosophy, it attempted to connect the unconnected, relying on mere visual puns and resemblances without regard to causative mechanisms (or perhaps, mistaking those analogies for a kind of mechanism itself). But thanks to the work of D’Arcy Thompson, and now modern scientific theories of complexity and pattern formation, a contemporary Neoplatonism has re-emerged as a valid way to understand the natural world. There are indeed real, quantifiable and verifiable reasons why zebra stripes look like the ripples of windblown sand, or why both the Giant’s Causeway and the tortoise shell are divided into polygonal networks. When we experience these objects and structures, we experience what art historian Martin Kemp has called “structural intuitions”, which are surely what the Neoplatonists were responding to. And these intuitions are what Peter’s work, with all its intricate balance of order and randomness, awakens in us.
To find out more: see Peter Randall-Page, “On theme and variation”, Interdisciplinary Science Reviews 38, 52-62 (2013) [here].