Applications of Fractals
MoleculesIn addition to anatomical structures, fractals were found in living organisms on even smaller scales ó in molecules.
As you probably already know, DNA is a long sequence of nucleotides that code all the genetic information about us. The nucleotides can be either adenine, guanine, cytosine, or thymine (abbreviated A, G, C, and T). One of the fractal patterns that were studied was in the sequence of nucleotides in what is called the DNA walk. The DNA walk is a graphical representation of the DNA sequence in which you move up if you hit C or T and down if you hit A or G. For example, for the sequence CATG you will get the following picture:
Fractal patterns were found in many DNA walks. These pattern are remarkably similar to Brownian motion. The fractal below is a model of a fractal DNA walk:
Chromatin is a fibrous material inside a cellís nucleus that contains the genetic material. As you can see below, chromatin tends to cluster:
We have seen on the example of galaxies, clusters are fractal in shape. Recently, scientists have found ways to measure the fractal dimension of chromatin. Interestingly, experiments performed a couple of years ago at the Mount Sinai research center in New York showed that the fractal dimension of chromatin might be somehow connected with cancer. Current experiments are attempting to detect breast cancer by measuring the fractal dimension. Talk about useful applications!
PROTEINS AND POLYMERS
A polymer is a molecule that is composed of a series of "building blocks" (called monomers) connected to one another in a chain. If you take a polymer, you will find that its monomers are not connected in a straight line. Instead, the angles between the monomers can be different and the entire molecule can twist into pretty complicated shapes. The same is true for proteins, which are formed by amino acid bonding together in a chain. Twisting, as well as folding and breaking often implies by itself that the shape is fractal. Proteins and many other polymers are, indeed, fractal and various methods exist for finding their fractal dimension. For some interesting proteins the results are shown below. Note that the dimensions are much higher than 1, which you would expect from a linear chain. This is another proof that proteins are fractal.
|Hemoglobin (oxygen carrier in the blood)||
|Myoglobin (muscle protein)||
If you hold a substance above in the flame, the flame will turn some color that is characteristic of that substance. If you then let the light from that flame pass through a spectroscope, the light will break into several colors of the rainbow. Shortly after the discovery of fractals, Harter found spectra of some molecules that remarkably resembled the Cantor Set. The picture below if a simulation of a spectrum that is perfectly fractal:
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.