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Fractals in Nature I: Trees

Y shaped tree branches, also known as tree forks, come about when a tree bifurcates, giving rise to two branches of roughly equal size.

Since photosynthesis is a primary form of energy, trees will use their sensors to move towards the light and away from gravity in order to enable their leaves to get maximum amount of life. However, there is an interesting intersection of math and nature here.

These branches are a prime example of natural fractals. Mathematician Benoit Mandelbrot, in 1975, defined a fractal as 'a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.'

The fractal nature of trees serve an important purpose including species identification, calculating amount of CO2 released into the atmosphere and how much water transpires through leaves.

Influences of y-shaped branches can be seen in architecture like Shanghai's Pudong International Airport and Tianjin Binhai Cultural Center, China as well as in coding. In C and C++ the command fork() when called will spawn processes as leaves of a growing binary tree.

Fun fact:

Da Vinci's Rule of Trees states that - All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk.

Sources:,, Structural Design Against Deflection by Tianjian Ji, The Art and Math of Tree Fractals by Gabriel Hemery


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