ALGORITHMIC BEAUTY

Dick Pountain/ Idealog 234/ 7th Jan 2014

The day I was due to write this column I had the good fortune to be visiting the Caribbean island of Bequia, and very nice it was too, with sun, sea, sailing boats, flowers and tropical fruit. However so advanced is my pathological nerd-dom that the subject it inspires me to write about is fractal geometry, rather than gastronomy, fishing or the miraculous qualities of modern sailing vessels.

Actually to a proper nerd this connection is pretty straightforward. We sailed to Bequia across a sea covered in fractal waves and spattered with fractal foam and spray, under a sky full of fractal clouds. And the land is covered by a profusion of the most fractal plants imaginable, from palms to frangipanis to ferns and back again. In fact it was while inspecting some palm fronds on the beach that I was suddenly reminded of a book that impressed me very much when it came out a quarter of a century ago, called "The Algorithmic Beauty of Plants" by Przemyslaw Prusinkiewicz and Aristid Lindenmayer (Springer 1990). The authors, with expertise in mathematics, biology and computer graphics, set out to model the forms found in real plants using a system of fractal geometry call L-systems, which mimics the development of a plant. It operates with a smallish number of parameters that can be varied to produce a vast range of startlingly realistic plant forms - stems, leaves flowers and all.

Their key insight was that the form a plant exhibits is not a static fact but something dynamic, generated during the process of growth, and in this respect they brought the brilliant work of D'Arcy Thompson into the computer age. That insight can be summed up by saying that each form implicitly contains its own history. Of course Prusinkiewicz and Lindenmayer were only simulating such a history inside a computer, but the results are so realistic one can't help wondering whether they provide a clue to the way Nature itself does it.

Clearly Nature doesn't type in the algorithms that Prusinkiewicz and Lindenmayer describe in C++ code, nor even in pseudo-Pascal. There is no need to postulate a nerdish Intelligent Designer with beard, keyboard and Tux-the-penguin teeshirt. All that Nature has available to work with is chemistry, and dynamic chemistry at that. Such chemistry is now pretty well understood thanks to the likes of Ilya Prigogine, who explained how factors like gradients of concentration or temperature can cause a chemical system to oscillate regularly in time, like a clock. As a plant stem is sprouting biochemical processes inside each of its cells cause the levels of certain growth hormones to vary cyclically over *time*, with the result that leaves pop up in a *spatial* sequence along its length. Put another way, Nature is its own hybrid digital/analog computation system, in which the rates of such chemical cycles, following various power laws, cause behaviour that somewhat resembles Prusinkiewicz and Lindenmayer's algorithms.

And the way plants and animals vary those growth parameters is only very loosely determined by the quaternary digital code of their DNA. A class of genes called "homeobox", present in all multicellular lifeforms, determine only the broadest divisions within the creature's form, like its number of limbs or body segments - all the finer details get determined by these semi-autonomous chemical cycles and various epigenetic factors.

One of the stronger arguments the Creationist and Intelligent Design brigades can muster is that the fierce complication of the way nature looks and operates is too great to all be encoded statically in the finite amout of DNA. But in fact it doesn't have to be all so encoded. Indeed the whole metaphor of a designer working from a total blueprint misses the way that Nature actually works. Nature and evolution are dynamic, non-deterministic systems in which stuff continually happens and affects other stuff, and this couldn't possibly be captured in any static plan. The Deist notion of a God who just pressed the Start button and then withdrew forever is far closer to the truth than any active designer.

Nature's "blueprint" is more like a thick wad of blueprints for tiny clockwork protein machines that, when set to work, rush around interacting with one another and with their external environment, and the end result is all this marvellous beauty and diversity that we see. If you can get your head around the idea of (never the details of) such fantastically complex chains of causality, they are actually far more marvellous than any hypothesised Intelligent Designer. In fact having to invent such a creator, while useful and necessary during the infancy of our species, has nowadays become merely a lazy copout that insults our human ability to understand the world we live in.