One of his observations referenced the fractal growth pattern of trees :
"Leonardo claimed that each year when the branches of plants have concluded their maturation, when added together, the sum total of their cross-section is equal to the cross-section of the trunk." Enlarge the thumbnail in this page to see a scan of his sketch ...
... and here's a piece of modern art generated mathematically by following this principle.
Some trees exhibit it better ...
A mathematical model created last year questioned the long-standing theory that the fractal form of trees evolved to allow optimal sap flow and proposed instead that this growth pattern is dictated by wind forces.
|My cherry blossom tree demonstrates wind resistance in the summer|
Trees are an example of covergent evolution. This is when, through generations, unrelated species find the same solution to their problems. Different plants discovered that by developing trunks, they could reach higher, even shading other plants competing for sunlight. The first plants to evolve in this way were similar to tree ferns (with trunks but without branches) or pines with whorls of radial branches around the length of their trunks with minimal signs of further branching.
The next evolutionary steps for trees in climates where there are clearly defined seasons were that the lower branches grew upwards to form crowns for more exposure to light in sunny months, and the trees lost their leaves in wintery months resulting in reduced surface area to prevent damage by winds and snowfall.
This is my favourite tree in a public place. I posted photos of it in autumn while its leaves were still intact and last month when it was covered in snow, but here it is on a sunny day at the point where winter turns to spring. Please take a walk with me to the tip of the longest branch on the right and then ...
In autumn I didn't know its name, assuming it was a type of chestnut tree.
Its prickly, green fruit were so hard that they wouldn't break under-foot when I trod on them to check if there was a nut inside.
Now they have turned golden-brown and softened to a multitude of fluffy tufts each carrying a seed.
I eventually classified it by the markings on its branches.
The London plane (platanus hispanica) is a hybrid of platanus occidentalis (American sycamore) and platanus orientalis. It's more resistant to fungal disease compared to its parent trees and thrives in urban areas as it self-cleanses. Its relatively stiff outer bark sheds as the tree expands, removing residual pollutants with it and producing a mottled effect which inspired the khaki pattern used for military uniforms.
I'll return later in the year to see what its flowers look like. I've read that they're inconspicuous, facilitating wind pollination, as these trees belong to an ancient family which evolved before bees and butterflies. Maybe this also explains its strange branch formation, half-way between a fir tree's and a regular deciduous tree's (as in Leonardo's sketch).
He noted that the fractal principle only applies to trees that aren't deformed or haven't been pollarded. Since classifying this tree I've seen several around, they all have symptoms of an irregular (not deformed) shape though they're not as old as the tree above. Maybe he wasn't aware of plane trees ...
I felt uncomfortable publishing this post because it seemed that I had left a loose end, but relaxed after reading these words :
The elements of mathematics, that is to say number and measure, termed arithmetic and geometry, discourse with supreme truth on discontinuous and continuous quantities. Here no one argues that twice three makes more or less than six, nor that a triangle has angles smaller than two right angles, but with eternal silence, every dissension is destroyed, and in tranquility these sciences are relished by their devotees.
― Leonardo da Vinci
I think he's saying that mathematics is just a way to simplify a complex world. Sometimes the rules apply and we can use them to help us learn more; sometimes they don't.
The references that I used for this post can be found by clicking on the blue writing.
Today I'm treading in the footsteps of these tree-bloggers Laura@patiopatch, Donna@gardenwalkgardentalk and Lucy@looseandleafy.
I'll be following this tree through the seasons and linking in with Donna Abel's Seasonal meme.