Mathematical Fractals in Nature

Structures in nature and art that are based on mathematical fractals are always self-similar because they are hierarchical, meaning that patterns keep repeating themselves on a different scale. For example, a tree has a hierarchy with a trunk being one of its levels, main branches another level and so on.

Nature can produce fractals of a very strict order. In them, each level is a precise representation of the previous one reduced in size. One of the really captivating plants is cauliflower, which consists of at least three levels of the versions of themselves.

Typically, items that are based on fractal geometry are limited in size because objects become smaller and smaller and can’t stay indefinitely fine when it comes to their details. You can’t have trees that are as big as mountains, which is why all natural and art objects of fractal structure only range over a range of scales.

However, some mathematical fractals keep their shape no matter how small they get. Fractals in nature, such as shorelines and mountain ranges, are an outcome of the process of gradual erosion. The opposite process, a steady accumulation, can also result in the creation of unpredictable fractal shapes. Mineral dendrites that lace through the rocks have very irregular forms, yet are an example of a fractal structure. Fluffy particles of soot created by tiny blobs of carbonized materials can also form fractal clusters through a process of aggregation.

Fractals don’t necessarily occupy all the space that is available to them. Filling the space is not their goal. Fractal structures are so common in the world around us that researchers have believed for a long time that they serve some goal. For example, in human lungs, the bifurcating passages exist to distribute vital elements to the cells. This is also what happens with many plants. Networks created by fractals distribute air, blood or some other substance.