Mandelbrot fernfernComplexity Pages
A non-technical introduction to the new
science of Chaos and Complexity

Victor MacGill
Victor MacGill
link to Victor's homepage
Email Victor

On this Site

Go to tutorial A basic tutorial about chaos and Complexity which covers the main topics.
 

Go to tutorial A booklist of books covering various aspects of Chaos and Complexity

Go to tutorial Articles written by Victor involving aspects of Chaos and Complexity

Go to tutorial Web resources and links

 

A glossary of Terms about Chaos and Complexity A Glossary of Terms used in Chaos and Complexity from http:// www.calresco.org

A glossary of Terms about Chaos and Complexity Search this site

The Mandelbrot Set

Dissipative Systems




Chemical reactions usually form equilibrium systems. When chemicals mix they typically undergo a reaction and change into other chemicals. After the reaction, the chemicals settle into a new equilibrium state and the chemical system then stays in its new equilibrium state. At this equilibrium point, the concentration of all the new chemicals created remains the same and the system does not change again without a perturbance from the outside. Chaotic systems, including all living systems do not exist at equilibrium because they do not stay the same. For living organisms, equilibrium means death. Chaotic systems are said to exist “far from equilibrium”, describing the dynamic nature of their stability, where the forces of entropy that would collapse the system are overcome.

Think of a person running. If we were to “freeze-frame” the runner at any point within their running cycle, they would fall and probably hurt themselves badly. We do not usually fall over when we run because running is a dynamic process. Provided we continue to inject energy into the system and maintain the pattern of motion, the runner can sustain the activity in a way a static system never can. Life is a process rather than a static state. The tightrope walker mentioned above is another example. Provided the tight-rope walker continuously rebalances, they can walk along the rope and reach the other side.

Organic complex systems live by absorbing energy from the outside environment, through the system boundary, and drawing it into the organism. That energy is used to sustain itself. Energy that is no longer required or will have a negative effect on the sustainability of the system is released back into the environment creating a flow of energy through the system. Some form of work is done which affects the outside environment.

Illya PrigogineSuch a system is called a dissipative system. The Russian chemist and Nobel Laureate, Ilya Prigogine began work exploring these systems back in the 1960s. They are “far from equilibrium”, and require a flow of energy to maintain themselves.

Even water flowing in a stream can form a dissipative system. Water flows from upstream and takes a particular shape in the stream, with swirling eddies and flows of water depending on the shape of the bottom and the nature of the water flowing. As long as the flow remains constant and the shape of the riverbed is unchanged, the water will maintain the same shape as it flows over the rocks. The water forming the shape is always changing as water flows through, while the shape remains the same. A cyclone or a tornado is also a dissipative system. A cyclone can remain as an identifiable separate object, but the air that makes up the cyclone is continuously changing. Air from the outside gets sucked in and after swirling around within the cyclone, leaves it, to be replaced by more air.  The form of the cyclone is sustained, while the air that makes it up continuously changes.

A cell in our body is a dissipative system. It absorbs energy into the cell in the form of molecules derived from food eaten or liquids drunk, which is then used to sustain itself, and releases unused or toxic wastes. A cell, like all living systems, is dissipative like a water flow or a cyclone, but has the extra property of having a more distinct boundary or membrane.

A human body is made up of trillions of cells and yet a whole human body also acts as a one dissipative system in its own right. Our skin forms a boundary between us and the outside world. We take in food and water and excrete urine and feces. We maintain our bodily form while the atoms that constitute our form are constantly changing.

Other less material systems operate as dissipative systems. A city has a defined boundary. Energy comes into the city in many forms, electricity, water, food, information, money, building materials etc. Rubbish, goods, information and other items are taken out of the city. Again, the form of the city remains the same even though the inhabitants, businesses, the buildings and other parts of the city are constantly changing.

The boundary must be a dynamic boundary, able to allow in what is needed for the survival and maintenance of the system while rejecting anything that will be detrimental to the system. Further than that, the system must be able to create and maintain the boundary itself. It can not be created from outside, but needs to be created from material within the system. The system can then repair and maintain the boundary.

Previous Full Tutorial Next    |     Previous Quick Tutorial Next



© Victor MacGill 2007, This site is a part of the web site of Victor MacGill.
The disclaimer on that site applies equally to all pages on this site.