The natural world is resplendent with patterns: clearly visible, and intrinsic regularities of form that are manifest, for example, as symmetries, branching fractals, tessellations, waves, meanders, cracks, foams, stripes and spirals. Indeed, the logarithmic spiral is a constant feature across a massive range of scales, extending from the fossil dimensions of ammonite shells, through the swirling fury of hurricanes, and upward, to the rotational immensity of stars in a spiral galaxy. In this lavishly illustrated book (which follows on, admirably, from his ‘Shapes: Nature’s patterns’ trilogy), Philip Ball demonstrates that a picture truly does ‘paint a thousand words’, in which he takes the enquirer, and seeker of beauty, through a gallery of images from all, ‘animal, vegetable and mineral’, that both please the eye and question the mind as to why particular patterns appear to pervade, universally, the set of tangible structures that we observe. At a very fundamental level, the relatively restricted set of observable design elements arises from an underpinning set of organizing, and opportunistically acting, forces that serve towards achieving growth, and establishing equilibrium.
Ball opens our journey with the fact that seeking order and regularity is ‘hardwired into our brains’ and helps us to survive and make our way in the world into which we are born. Symmetry is the fundamental language of pattern and form and is not built up into the shapes that we observe in nature, but these are instead created by the fragmentation of uniformity (‘symmetry breaking’); thus, patterns (e.g. those often represented on wallpaper or Persian rugs) arise from the partial disintegration of symmetry. Bilateral symmetry appears to be an almost ubiquitous default shape for animals, fish, insects and birds and is said to be a feature of attractiveness in human faces, while other animals with more symmetric bodies than their rivals tend to have more sexual partners. Remarkably, molecules, particles, grains, rocks, fluids and the tissues of living creatures all have a tendency to arrange themselves into regular, often geometric patterns, apparently unbidden. Through progressive processes of symmetry breaking, patterns of increasing sophistication and elaborateness are generated, of which Ball presents many and various, striking examples, including the face of a tiger, which well countenances William Blake’s resounding challenge in the final line of his poem ‘The Tyger’: ‘what immortal hand or eye, dare frame thy fearful symmetry?’
Fractals provide the next stop on our perambulations, which we see manifest in the filigree of trees, extending outwards in a sequential, progressive branching, while the ‘length’ of a coastline can be seen to extend increasingly, as an aerial view of it reveals a hierarchical repetition of the same elemental structural form when perceived at scales of increasing magnification. Indeed, the fractal branching of the lungs, which assists their essential function to exchange gases with fluids – the efficiency of which is enhanced as the surface area increases – is reminiscent of the fractal form of trees, which also exchange gases between the fluids they contain and the atmosphere. Mirroring the growth above ground, in the soil, beneath the ground, the roots of trees also reveal a fractal form, which is extended further by a symbiotic association with mycorrhizal mycelia – of similar appearance to the spatial neural networks in the brain – which vastly enhances the effective surface area of the root system, and hence the uptake of water and nutrients by the plant roots. (Such fractal branching in living systems also builds in bypasses which allow the system overall to continue functioning even when it has become damaged in some way; thus, modelled on the patterns and behaviour of natural systems are derived two of the design principles of permaculture, that ‘each element performs many functions’ and ‘each important function is supported by many elements’. The design is ‘resilient’ if critical functions are supported in a number of different ways and continues to operate should any one element of the system fail). It is surprising that such fractal branching is also to be seen in mineral dendrites, formed on limestone surfaces by a lattice reaction–diffusion mechanism: although with no equivalent function to these other (biological) examples, the growth processes in all cases probably share a common instability that drives a constant repetition of branching at the network tips.
Rhythmical processes of erosion and deposition form the familiar sinusoidal ‘meander’ of a river bed, which can be explained in terms of fluid dynamics. Although the particular forms show considerable diversity, they are typically networks that disperse the energy of the flowing water at the most rapid rate possible. Other authors have presented accretion as a fundamental evolutionary mechanism, common to the development of biomolecules, cities and entire galaxies – and by implication many/(all?) processes of intermediate magnitude – thus the concept is profound. So, these same basic forms seem to occur/repeat in sand dunes, galaxies, DNA, ammonite shells and so on, presumably also underpinned by forces of accretion acting at different dimensional scales. Despite a broad understanding, and mathematical formulation of the mechanics that drives the formation of the different patterns, many of the details were elucidated only comparatively recently, for example, the creation of the unique, hexagonal symmetry of a snowflake. It is remarkable that ice crystals (formed merely by the condensation of water molecules from air, to form a solid structure) can become so arranged that each arm of a snowflake is practically identical, almost as through a form of communication is going on between them to create each particular unique pattern.
Of the other natural patterns, spirals may be seen to represent a logarithmic process of expansion and contraction: a monad of form with the ability to furl and unfurl, onwards and forever. Waves are not static patterns, since they also propagate through time, and are apparent in stormy seas and skies, and in oscillating chemical reactions: famously, the Belousov–Zhabotinsky reaction. The murmuration of starlings follows (or generates) a wave that oscillates through flocks of thousands and probably serves either to prevent individual birds form colliding in flight or to act as an alarm signal when predators are near. Bubbles and foam are found to observe a precise harmony between various shaping forces that stretch or push them into gentle curves and frameworks. The hexagonal arrays of cells in a beehive honeycomb are created from the interaction of physical forces that are inherent in nature, while the junctions between the foam bubbles, in a soap film, are usually of fourfold symmetry, with the four edges pointing approximately towards the corners of a tetrahedron. Discernible patterns occur too, when formerly wet ground dries out, to form a landscape filled with cracks. In this case, a tension gradient is created by the shrinkage of the drier layer at the surface, relative to the still-moist layer below. The ‘cracks’ that appear in the sky when a bolt of lightning strikes are also not random but possess structure and pattern, as does the fractured flow of a river: that such disparate examples, nonetheless, broadly resemble one another might suggest the existence of certain underlying commonalities of the patterning processes that shape the natural world.
It is thought that the formation of Turing structures might be an underlying factor in the patterning of a fertilized human egg cell, as it grows and divides, and also in the patterns that are apparent on the skins of some animals, and those possessed by certain insects. However, the undulating forms created in non-living media, such as sand dunes by the wind, may also involve Turing structures. In some semi-arid regions of the globe, unusual patches of vegetation have been discovered growing in otherwise bare ground, which also appear to be underpinned by a Turing type process.
The numbers and kinds of patterns being discovered increases relentlessly, as observation reveals further intrinsic features of the natural world. Having read and marvelled at the many and splendid pictures in this book – which would grace any coffee table and inspire joy and conversation, but is far more than this – the reader will begin to see new patterns in many aspects of their lives and the world around them and be further inspired by the consummate wonder of who and where we are, in nature and in the universe.
Christopher J Rhodes
Fresh-Lands Environmental Actions, Berkshire, UK
Email: cjrhodes@fresh-lands.com