Picture 1: The initial branch on this tree is several feet long but the pairs of branches that then emerge are shorter in length. Photo by Robert Dryja
By ROBERT DRYJA
Los Alamos
Winter can be good time to see how trees grow since their branches are free of leafs. Branches grow in different ways depending on what they are doing to help the tree grow. The branches may weigh hundred of pounds in a large tree. The primary purpose of the trunk emerging from the ground therefore is to support the rest of the tree. A trunk grows vertically since the weights of the branches above it now are directed downward. A trunk leaning to one side would tend to weighed downward as a result of the branches now growing on that side.
The trunk emerging from the ground could be called the primary trunk. Relatively large branches grow from the primary trunk and could be called secondary trunks. These secondary trunks support a portion of the branches growing out of them. Both the primary and secondary trunks may be identified by the rough bark growing on them. Two to five secondary trunks may be present depending on the size of the tree and how long it has been living. What could be called true branches emerge from the secondary trunks and can be identified by having smooth bark.
Primary branches typically divide repeatedly into pairs of smaller secondary branches, (see Picture 1). The angle between the initial pairs of secondary branches can be relatively small, perhaps 20 degrees. The angle then can become greater for other pairs growing further along a primary branch. The smaller secondary branches that emerge from repeated divisions now have a different purpose. They are concerned with supporting leaves and flowers, not supporting weight. The angle between pairs of branches increases and can approach 180 degrees, or nearly a straight line. The increased angle means that branches now grow away from each other rather than remaining close together.
Robert Dryja
The length of pairs also decreases along the branch. A pair of branches may be a couple of feet in length at the initial dividing of branch into two. However, it may be only an inch in length after several divisions have occurred, (see Picture 2). These small branches often are called twigs.
The twigs grow so that leaves or flowers can receive as much sunlight as possible or be more visible to birds and insects. Supporting weight is no longer the primary concern. The lighter weight and shorter length means that a form of geometry becomes more apparent. Fractal geometry involves a form of math in which a pattern is repeated. A repeating pattern remains the same but becomes smaller in size along its length. Mathematically, there is no end to the length. The curves seen in tree branches reflect the geometry involved, (see Picture 3).
Curves also are a result of biologic growth to reach as much sunlight as possible, not only to follow a mathematical formula. Other ecological factors are at work. Branches may grow more or less from year to year depending on the seasonal weather conditions. Little growth may occur when an exceptional dry season occurs. Branches that point toward sunlight may grow more compared to branches facing away. The predominant direction of wind also may influence the direction of branches face.
Picture 2: The growth of a twig on a tree can be very similar to a fractal math pattern. Courtesy/Fractal Foundation
Picture 3: The growth of a twig can be very similar to a fractal math pattern. Courtesy/Fractal Foundation