The Incompleat Naturalist: The Architecture of Trees

A towering Giant Sequoia (Sequoiadendron giganteum) in
Yosemite National Park, California. Giant Sequoias are among the
largest trees in the world. The huge trunk of this tree reaches about 200 feet
before branching.

Winter is a great time to admire the architecture of trees. Deciduous trees dropped their leaves in the fall and their structure is on display for all to admire. The variety of tree shapes is astounding. Some trees have towering trunks with their branches high in the air. Others are small with multiple trunks. Some trees look like vases or columns or pyramids, some weep.

A Bald Cypress (Taxodium distichum) with the pyramid shape.
Like Christmas trees, this Bald Cypress is widest
at the bottom and tapers toward the top.
Rowan County, North Carolina.

A Red Maple (Acer rubrum) with many trunks growing from the base
giving it a vase-like shape. Rowan County, North Carolina.

Dwarf Weeping Cherry (Prunus subhirtella). This small tree has
a short trunk and numerous contorted branches. The terminal branches
hang down and the tree appears to weep.
Rowan County, North Carolina.

The branching pattern of trees has much to do with their shape. Leonardo da Vinci, when he was not painting the Mona Lisa, designing helicopters or making breakthroughs in human anatomy, considered the branching of trees. His fundamental insight about trees is that the cross-sectional area of the trunk is equal to the cross-sectional area of the branches. So, if the main trunk of a tree has a cross-sectional area of 100 square inches and it branches into two main limbs, those two limbs will have a cross-sectional area of about 50 square inches each. This pattern continues with all subsequent branches. If you measure the cross-sectional area of the twigs they will still have a cross-sectional area of 100 square inches.

Black Gum (Nyssa sylvatica) with a main trunk
and many limbs with branches. Rowan County, North Carolina,

Consider the branching of trees. A branch may divide into two branches and each of those branches could branch into two more branches. This pattern is repeated many times in a tree. Iterative branching goes a long way in explaining the shape of trees. Trees are natural examples from the field of mathematics called fractal geometry. The Polish-French-American mathematician Benoit Mandlebrot coined the term fractal in the late 20^th century to describe objects that have similar structure at different scales. If you look at a whole tree, you find the same basic pattern in the limbs, branches and twigs.

A fractal tree. Virtual trees like this can be produced by a
couple of dozen lines of code. This mathematical tree bears
a striking resemblance to a biological tree.
https://commons.wikimedia.org/wiki/File:Fractal_canopy.svg

The fractal branching pattern of an American Sycamore
(Platanus occidentalis). Rowan County, North Carolina.

Fractal tree canopy in winter. Rowan County, North Carolina

The reason a tree makes all those branches is to provide the scaffold for the leaves. A large tulip poplar tree (Liriodendron tulipifera) may have over 100,000 leaves. Each leaf weighs only a few grams but during summer, particularly when the leaves are wet and the wind is blowing, they put a tremendous stress on the tree. This load is supported by up to fifteen tons of wood in the trunk, limbs and branches.

Leaves of Tulip Poplar (Liriodendron tulipifera) in high summer.
The hundreds of thousands of leaves are supported by the many
small branches of the tree.

Some trees have tall straight trunks and limbs extending out to the side. Pine trees (Pinus sp.) are good examples of this structure. When a side limb dies or is broken off, the tree continues to grow in diameter until the broken limb is entirely overtaken and is now inside the trunk. This old limb may be invisible from the outside but, if the tree is converted to lumber, the old branch is seen as a knot in the wood.