Applications of Fractals
If you are still not convinced that that fractals, being a math topic, are very important in real life, your opinion might change after finding out that you yourself are made of fractals!
The first place where this is found is rather obvious to anyone who knows fractals — in the pulmonary system, which you use to breathe. The pulmonary system is composed of tubes, through which the air passes into microscopic sacks called alveoli. The main tube of the system is trachea, which splits into two smaller tubes that lead to different lungs, called the bronchi. The bronchi are in turn split into smaller tubes, which are even further split. This splitting continues further and further until the smallest tubes, called the bronchioles which lead into the alveoli. This description is similar to that of a typical fractal, especially a fractal canopie, which is formed by splitting lines:
The endpoints of the pulmonary tubes, the alveoli, are extremely close to each other. The property of endpoints being interconnected is another property of fractal canopies.
Another supporting evidence that your lungs are fractal comes from measurements of the alveolar area, which was found to be 80 m2 with light microscopy and 140 m2 at higher magnification with electron microscopy. From the geometric method we know that the increase in size with magnification is one of the properties of fractals!
THE BLOOD VESSELS
Similarly to bronchial tubes, splitting can also be found in blood vessels. Arteries, for example start with the aorta, which splits into smaller blood vessels. The smaller ones split as well, and the splitting continues until the capillaries, which, just like alveoli, are extremely close to each other. Because of this, blood vessels can also be described by fractal canopies.
The surface of the brain, where the highest level of thinking takes place contain a large number of folds. Because of this, a human, who is the most intellectually advanced animal, has the most folded surface of the brain as well. Geometrically, the increase in folding means the increase in . Instead of 2, which is the dimension of a smooth surface, the surface of a brain has a dimension greater than 2. In humans, it is obviously the highest, being as large as between 2.73 – 2.79. Here’s another topic for science fiction: super-intelligent beings with a fractal brain of dimension up to 3!
The surface folding similar to that of a brain was found in many other surfaces, such as the ones inside the cell on mitochondria, which is used for obtaining energy and the endoplasmic reticulum, which is used for transporting materials. The same kind of folding was found in the nasal membrane, which allows sensing smells better by increasing the sensing surface. However, in humans this membrane is less fractal than in other animals, which makes them less sensitive to smells.
The fractal dimension of some anatomical structures are given below. Note that all dimensions are greater than you would expect them to be, and most are fractions, which automatically implies that the structures are fractal.
very close to 3
2.73 – 2.79
|Mitochondrial Membrane (outer)||
|Mitochondrial Membrane (inner)||
Fractals, in addition to the anatomical structures above can be found in the body on smaller scales in various molecules.
Geometry in Biological Systems : An Analytical Approach
Philip M. Iannaccone(Editor), Mustafa Khokha (Editor)
Although extremely hard to read, this book is an excellent collection of the most exotic applications of fractals. The topics touched come from practically all areas of biology, from DNA structure to the heart rhythm.