In complex systems, such as weather patterns like Hurricanes and Tornadoes, to track the small changes in the variables that occur as the system’s chaotic behavior travels along the ‘arrow of time’, scientists have developed chaos theory.  Fractal patterns are one of the tools used as a feedback mechanism in the patterns of ordered chaos through the principle of iteration, or repetitive changes.  These repetitive changes require huge amounts of calculations on mega-computers, as even the tiniest change is magnified over the number of calculations that are required, in order to even attempt to predict the weather.

Here’s what the research paper “Fractal Behaviour of Complex Systems”,  had to say about the subject:

“One of the most important properties of systems is complexity. In a simple way, we can define the complexity of a system in terms of the number of elements that it contains, the nature and number of interrelations and the number of levels of embeddedness. When a high level of complexity exists in a system, it is considered a complex system. Complex systems can be soft systems and hard systems. In hard systems, when their elements are interrelated in a non-linear way, they are considered complex systems when they contain a great number of elements interacting in a non-linear way. To try to understand the behavior of this type of system diverse mathematical tools have been developed. A new scientific discipline with great impact in the analysis of the complex systems has been developed in recent years, called fractal analysis. The study of the complex systems in the framework of fractal theory has been recognized as a new scientific discipline, being sustained by advances that have been made in diverse fields ranging from physics to economics. In this paper the history and the basic concepts of the fractal analysis of complex systems are discussed briefly and an oil crude price volatility fractal analysis is provided.                                     Copyright © 2009 John Wiley & Sons, Ltd.

For more on this paper, visit:

http://onlinelibrary.wiley.com/doi/10.1002/sres.984/abstract

Similarly, while researching this topic, I came across the following information from Nagai Toshiya - http://www.nagaitosiya.com

1. You cannot reduce the whole to parts but to rules.
2. They are brought about by self-referential repetitive application of simple rules.

Modern scientists have analyzed objects by reducing an unintelligible whole to intelligible parts. But when the unintelligible whole is composed of similarly unintelligible parts, reductionism proves to be helpless.

In a real nature however it is linear algebra that is exceptional and most of nature has a fractal structure.

Chaos also refuses to be reduced to parts. Most of chaos including Lorenz attractor has a fractal structure. Its "strange" whole can be reduced not to parts but to rules.

Makes one really think about the nature of the universe…