Leonardo's Rule of Trees
Leonardo drawing. The British Library.
I once watched a TV programme with the professionals who made it. This was on the ill fated TV AM (saved by Roland Rat) where a friend was a make up artist. She scrutinised her work and only her work. Her colleagues scrutinised their work and only their work, sound, camera, lights, set, graphics, you get the picture.
Also, once (bear with me) having been lucky enough to go into the tomb of Tutankhamun in the Valley of the Kings, I was granted access to the Howard Carter Papers - sketches, diaries, diagrams, index cards and personal notebooks.
In the room were Egyptologists, each an expert in his/her own field on the jewels, musical instruments, board games, statues, gods, hunting weapons etc., found in the tomb.
Reading recently about experts in their own particular fields trawling through Leonardo's Notebooks, those two experiences sprang to mind.
Dendrologists, who study the growth patterns and structures of trees, say that Leonardo's Rule of Trees is spot on.
'Every year when the boughs of a plant [or tree] have made an end of maturing their growth, they will have made, when put together, a thickness equal to that of the main stem; and at every stage of its ramification you will find the thickness of the said main stem; as: i-k, g-h, e-f, c-d, a-b, will always be equal to each other' *
Apparently, our ability to recognize trees in art, even in abstract art, is because of simple maths: The Branch Diameter Scaling Exponent.
Leonardo loved Maths. In 1495, he and Milan's famous mathematician, Luca Pacioli, collaborated on Divina Proportione (mathematical principles of the golden ratio).** Leonardo illustrated it. They had probably read Euclid who was the first to notice it in 300 BC.
Leonardo filled Notebooks with his theories on geometry in Nature e.g. the angles at which tree branches grow from the trunk.
Almost five hundred years later (1975) what he was describing was coined in a new, made up, name. Mathematician, Benoit Mandelbrot, called patterns in nature, fractals (from Latin fractus, fractured).
The best way to start a row is to publish a scientific paper.
Other researchers say that Leonardo's Rule of Trees is wrong.'The older Leonardo rule describes the thickness of the branches, while the length of the branch was not taken into account.'
Not only did they use 3D modelling and computer simulations not available to Leonardo they even had the cheek to call their finding The New Leonardo Like Rule.
Leonardo created his Rule for two dimensional representations of trees for artists. It's a safe bet that neither the for' nor the against' are able to blend science with the artistic skill which enabled the Master not only to discover hidden patterns in trees but to represent them in paintings. He was both scientist and an artist.
* Leonardo da Vinci's Notebook.
** In layman's terms: The golden ratio/number/proportion e.g. the way snail shells, seed heads. flower petals, pine cones are formed or of course, Leonardo's Vitruvian Man.
Post by Pamela (BA History of Art). Photography by Mark.
Pamela Shields
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