56. Sketch by a Cleark of the Works
Andre & Sleigh, Sc.
The illustration plate, ‘Sketch by a Clerk of the Works’, is taken from the end of the chapter ‘The Stem’ in Modern Painters Vol. V. The plate is included to illustrate the compositional rulings of changing curvature of a kind found in many natural forms: clouds, rocks and trees.
The illustration is an example of what the mathematician Benoît Mandelbrot would later term ‘fractal geometry’. In The Fractal Geometry of Nature (1982), he asks, ‘Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.’ Mandelbrot’s work would offer a framework for understanding geometry – and nature - differently: ‘fractal’ being a term for irregular mathematical shapes, with structures that are self-similar over many scales, and that infinitely repeat.
Over 100 years before the publication of The Fractal Geometry of Nature, Ruskin recognised the fractal quality of a tree: the trunk is the origin point, from which sets of branches grow, which become sets of twigs, which will eventually grow into bigger branches. Ruskin’s apprehension of fractal forms, grounded in a belief in the grand design of the universe by God, links nature and aesthetics:
‘But the form in a perfect tree is dependent on the revolution of this sectional profile, so as to produce a mushroom-shaped or cauliflower-shaped mass, of which I leave the reader to enjoy the perspective drawing by himself, adding, after he has completed it, the effect of the law of resilience to the extremities. Only, he must note this: that in real trees, as the branches rise from the ground, the open spaces underneath are partly filled by subsequent branchings, so that a real tree has not so much the shape of a mushroom, as of an apple, or, if elongated, a pear’ (LE 7 (1905)/84).
Reference. no. 1996B0561