Applications of Fractals
If you know some chemistry, you are probably familiar with the concept of forward and backward reactions. Most reactions are accompanied by a backward reaction, in which the products turn back into the reactants. At equilibrium, the rates of these reactions become equal and the overall composition of the system does not change. However, the fact that is usually missed here is that talking about the rates of reactions we are talking about average rates, since the rates depend on the movement of particles, which involves a lot of chance. Sometimes, however, the rates become different for a short interval of time and the composition of the system changes. As you might guess, these changes would be very chaotic... Aha! In one of the lessons, we have already established the connection of chaos and fractals. Maybe if we view every three consecutive concentrations of a substance as coordinates of a point in space... we can get something that is fractal in shape! Such fractal would be a strange attractor because we know that this is the type of fractals based on changing numbers.
Indeed, fractal shapes were found after graphing many different systems, even such common ones as hydrogen and oxygen reacting to make water. One of the scientists who tried to study this mathematically was Otto Rossler. He came up with three formulas that could model chemical reactions. When these three formulas are used to create a strange attractor, they create the famous 3-dimensional Rossler Attractor: