When I look at trees, I often find them beautiful, both their flowers and greenery, but I think I also find the shape of the tree itself beautiful. There seem to be some geometrical characteristics to the shape of a tree.
The Fibonacci sequence, a sequence of numbers that determines the next number by adding the previous two numbers, 0,1,1,2,3,5,8,13,…, appears in the number of petals on a flower, the arrangement of the leaves on a plant, the arrangement of sunflower seeds, the way cells grow, etc. In tree shapes, this sequence appears in the shape of a trunk that splits into two, then three, five, and eight as it goes up.
http://jumokukobe.blog.fc2.com/blog-entry-1107.html
The ratio of 1:1.618, also known as the golden ratio, which appears in pentagrams, seems to be found in nature. In tree shapes, the ratio of the length from node to node on a branch to the length from node to node seems to be within 1.5 to 1.8, and the ratio of the size of leaves seems to be within 1.6 to 1.7. The golden spiral created from a golden ratio rectangle seems to appear in the shapes of seashells and typhoons. The Fibonacci sequence itself is related to the golden ratio, and the ratio of adjacent numbers in the sequence converges to 1.618.
https://www.k-wam.jp/blogs/2018/05/post-22217
The golden angle of 137.5 degrees, which is 360 degrees divided by the golden ratio, can also be seen in pine cones, sunflower seeds, etc. In tree shapes, this angle appears in the way the branches grow when viewed from above, and it is said to be efficient at receiving sunlight.
https://gakuen.gifu-net.ed.jp/~contents/museum/golden/page62_3.html
When there are certain rules in the ratios, it often becomes a shape called a fractal, where the parts and the whole are similar. This seems to be seen in the leaves of ferns, coastlines, clouds, etc., and in tree shapes, the trunk and branches look similar when viewed from a distance to the look of a single branch and an even smaller branch when viewed up close. Fractals are also related to the power law, and the lengths of the branches in a tree shape follow a power law distribution. A shape consisting of one long trunk and many short branches is said to be characteristic of power law distribution.
https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-25891001
If we think of a tree shape as a structure with a trunk and branches, it seems that the roots and the veins of the leaves are also tree-shaped. Other tree shapes may also be the branching discharge shapes of lightning called Lichtenburg figures, the shapes of minerals formed in the gaps between rocks called dendrites, the branching of bronchi, blood vessels and nerves, and the branching of rivers.
https://museum.bunmori.tokushima.jp/bb/chigaku/minerals/34.htm
I looked into the background of the beauty of tree shapes and natural objects that take tree shapes, and I think it’s a basic form of growth and branching. Tree shapes are amazing. The shapes of the earth are amazing.
