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Leonardo Da Vinci's 'Rule of Trees'

Updated: Apr 27


A drawing of Leonardo Da Vinci's Rule of Trees
Da Vinci's 'Rule of Trees' was his observation of how trees grew mathematically in order to draw them more accurately.

Thank you for the Mona Lisa, Mr. Da Vinci, but what does art have to do with math?


I stumbled upon this observation that Leonardo Da Vinci came up with 500 years ago while Googling something else on trees. I'm sure there's a lot of you that already knew about this, but I was mesmerized by this concept. So, any of you who know me know that I'm a bit of a nerd when it comes to learning about things.


Leonardo Da Vinci's Vitruvian Man had a common thread with his "Rule of Trees'
Leonardo Da Vinci's Vitruvian Man

Have you seen this illustration of 'The Vitruvian Man that Leonardo Da Vinci was famous for? It's all over the place and has been ranked among the all time iconic images of Western civilization. The drawing represents Leonardo's ideal of body proportions. Looks like Leonardo wanted to have a similar representation for trees and how they grow.










So here's the gist of this 'Rule of Trees', and I'm quoting from a bunch of articles that I've found on the subject. Some scientists are claiming that Da Vinci's 'rule' is not complete. But for now, let's talk about Da Vinci's observations. Without getting too technical, it comes down to this: The total thickness of a tree's branches, when measured consistently where they grow off the trunk, almost always equals the total thickness of the trunk they have branched from. According to scientists, this helps the tree transport sap and withstand the wind. Da Vinci wanted to draw trees more realistically and it looks like he wanted to do it mathematically.


I have proof that the 'Rule of Trees' is accurate and here's why.


There was a stint of time when we were busy making art for festivals and exhibits. Accepted into several art festivals in the category of 'Sculpture', we created a whole lot of what I call 'wire Bonsai trees' using rocks as ballast and to represent the cliffs that so many trees precariously hang off of. I have always had a deep fascination for the trees I saw as a kid in Monterey California defying the elements, hanging off cliffs, wind-blown and twisted, growing in what appeared to be solid rock. This was my inspiration for the sculptures.


wire tree on volcanic rock art sculpture consistent with Leonardo Da Vinci's Rule of Trees
Sculpture entitled N.O.W. (Nixon Oliver Winward). My first attempt at wire tree sculpture

I really hadn't intended on making art pieces out of hundreds of strands of steel 18 gauge wire. It came about because a family member was throwing a shower for the their first grand-baby, my great-nephew. So of course there was a baby shower. I was asked to make something that represented 'The Giving Tree' (from the book) for party favors to hang on. Initially, it was thought that we could cut a branch off of a real tree and hang the party favors from that. But I worried about the stability of the tree with the weight of the party favors. I started brainstorming. I ran across a way to make a tree out of copper wire. My first little prototype tree ended up 3" tall. From there, I hunted for a rock that had some interest and a piece of green lava rock my dad had in his yard for years that I salvaged after he passed away was used to twist the roots of the tree throughout. The rock was full of holes and craters to anchor the wire roots. Well, it worked wonderfully. There was no way that wire tree was tipping over. By the way, this tree placed in a Sandy City Art contest. One of the first ones I've ever entered. As a side note, I wish I knew where my dad got this piece of lava rock. I can't find references of green volcanic rock anywhere.


So what's the point of all of this? Leonardo Da Vinci's 'Rule of Trees' theory is accurate. What you see in the photo above is the very first wire tree I made for the baby shower. The base of the tree is around 2" in diameter. There are around 250 strands of steel 18 gauge wire all at 7' long. I had to straighten a spool of wire on a frame I built out of steel pipe to straighten the wire so that each strand would lay orderly next to each other. All of those branches all of the way up to the ends, consist of the same 2" thickness. With very little deviation, the entire tree from the tips of the roots to the tips of the branches is 7 feet long. It may look asymmetrical and like one side of the tree is a different length than the other, but it isn't. All of the pieces I made followed the same formula, but varied in diameter and length to be size-appropriate to the rock it was paired with.


Wire tree set on rock consistent with Leonardo Da Vinci's Rule of Trees
The wires with my help twisted where they wanted to go to form a pleasing flow in it's pattern.

There was a huge learning curve as to how I would twist the steel wire. It was way harder to do with steel than copper. Copper is so soft and easy to twist. All the strands had to be twisted together at the same time in order to flow structurally. I had to get it to succumb into a flowing pattern, in a natural way, curving it in a logical rhythm as I twisted it. Even though I was guiding it, the flow of the wire strands followed a naturally aesthetic path relatively on its own. Kind of hard to explain, but I've found that the less things are forced into submission in art, the more beautiful it is. At least this was the case with my art. The simplicity in nature of an unburdened tree and the way it grows is so pleasing to the eye as it grows in an environment that presents little challenge. The form and structure of a tree in my opinion is art in it's purest form.


Leonardo Da Vinci's rule of trees displayed in Monterey Cypress
Monterey Cypresses in Monterey, California. I loved the structure of these trees even as a child.



But the tree in a survival situation such as one in harsh wind, fighting for nutrients, light and water, submits to force, yet the form it takes as a result is still just as beautiful, and even more meaningful and thought-provoking, because we, as observers realize there was hardship encountered. People who still have the grace and strength to be kind even after they've suffered adversity and loss, are like those trees.


There are mathematical sequences in music, and if you've ever taken music lessons, you know about the circle of 5ths. Order and design is undeniable and it's everywhere. It brings a sense of peace, whereas chaos and disorder brings frustration and stress. Maybe this is why it makes us feel so good to be outside, in nature, without all of the manmade chaos that you find in the places that we unfortunately, have to spend so much time. Amongst the trees, the living, growing things that, in reality, don't really need us to survive, we find tranquility. Quite literally, things that have been designed here on this earth to collaborate with each other are here in spite of us, as we try to manipulate what was thoughtfully designed and meant to be, into something unnatural and synthetic, unsustainable, to suit what humans so narrow-mindedly think is so important. We've become so distracted these days; we've lost sight of the most elementary axioms of what is truth, and has purpose.


Leonado Da Vinci wasn't the only artist whose works were mathematical
The Great Wave of Kanagawa by Hokusai.

One of the most recognizable pieces of art is 'The Great Wave of Kanagawa', created in late 1831 in the Japanese Edo period of history by the artist Hokusai. It contains fractals (mathematical repetition) throughout.






The Point of All This


Leonardo Da Vinci searched for formulas in order to draw a tree more realistically, and I think all in all, his discoveries benefited us, at least for 500 years up until now. What a mind he had. The way he thought, the things he created and discovered are simply genius. The more I learn, the more I realize just how much more there is to learn. The point of all of this, it had to be designed by shall we say, the source of art, the source of virtually everything.







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