Artwork name: Fractal Tree

Artist: Fractal Tree


Fractals: Koos Fractal Tree

Each branch in this tree has a square cross section and (except for the trunk)v it is cut off at 45° at the bottom, giving rise to a 1:v2-rectangular cut. At the other end, each branch (including the trunk) is cut twice at 45° v2, giving it a right-angled ‘roof’ consisting of two 1:v2 rectangles. Each roof rectangle accommodates the rectangular base of the next, scaled down, branch. The angle between a branch and each of its smaller offspring branches is 120°. In spite of this ’nice’ angle, it turns out that no two branches point in the same direction. It is a truly ‘wild’ tree.

The fractal nature of the tree can be appreciated by thinking of the tree as consisting of a trunk and two scaled-down copies of the entire tree attached to the trunk. It has fractal dimension 2 (even though the branches are 1-dimensional). Natural trees usually have a fractal dimension close to 2, because that way they can capture the most light, and it makes them strong and flexible enough to withstand violent winds.

In 1988 Koos wrote a speech about the importance of fractals titled "Chaos en de computer (chaos and the computer)". The speech is currently being translated for a publication with a collection of fractal images.


The term “fractal” suggests fracturing or splitting. Mathematicians use the term to describe a figure made up of an infinite number of parts, each part a scaled version of a single part, with the scaling constantly diminishing the size of repeated parts. Look closely at a fern, or a head of broccoli. These are finite, or partial, versions of fractals: when you look closely at the parts that compose them, the parts are smaller versions of the whole. 

A fractal can be created by beginning with a particular figure or shape and then following a set of recursive instructions. That is, an action is performed on the shape such as adding to it, or splitting it, which creates new smaller shapes similar to the original. The instructions are then applied to these new smaller shapes, and the process repeats again and again, ad infinitum. A fractal tree, for instance, can be created by splitting the original “trunk” into two thick branches that are smaller copies of the trunk. These two branches in turn each split in exactly the same manner, and the process repeats again and again as smaller and smaller branches grow on the tree.