IaaC blog

Group: Global Shopping

Sub-group: Pete Booth, Mariana Paz, Higinio Llames

Chaos 

Chaos is the complexity of causality or the relationship between events. This means that any ’seemingly’ insignificant event in the universe has the potential to trigger a chain reaction that will change the whole system. Chaos theory describes the behavior of certain nonlinear dynamical.

The name chaos theory comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.

So a simple, if slightly imprecise, way of describing chaos is chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random.

Butterfly effect

Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system. This kind of condition is usually known as Butterfly effect.

The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.

Group: Global Shopping

Sub-group: Pete Booth, Mariana Paz, Higinio Llames

You can download our PDF file here.

Mariana Paz Castellanos/Rodrigo Langarica Avila

Some of my mapping skeches…

http://www.imho.com/grae/chaos/chaos.html

 As a group our blogs were not very interesting, so we decided to look for a topic from wich we could get a lot of information and that it can be usefull for our proyects. So we decided to do some research about The chaos theory and Fractal geometry.

The name chaos theory comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.

Just a small change in the initial conditions can drastically change the long-term behavior of a system.
One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve.  A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure.

The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.

To get around this difficulty, mathematicians invented fractal dimensions. Fractal comes from the word fractional. The fractal dimension of the Koch curve is somewhere around 1.26. A fractional dimension is impossible to conceive, but it does make sense. The Koch curve is rougher than a smooth curve or line, which has one dimension. Since it is rougher and more crinkly, it is better at taking up space. However, it’s not as good at filling up space as a square with two dimensions is, since it doesn’t really have any area. So it makes sense that the dimension of the Koch curve is somewhere in between the two.

Fractal geometry reflects a lot of forms and behaviors in nature and artificially created. Since you take a look to something that apparently doesn’t have any relation, you will find that the same structure it is composed for the same form but in a minor scale.

For example by looking a map you will be able to find in the coast line several bays, but if you take a closer look you will see that there are some smaller bays that can only be seen by walking around, but the sand it also creates some smaller bays that we are not able to count, so this big structure it is composed by the same elements in a smaller scale, as it happens in the Koch curve.

There are also some other ways of discovering or creating a fractal geometry. The first image show a pattern created by a 3D software called chaoscope, but at the same time we are looking smoke that apparently create the same structure. One has been digitally generated, but the other one we can say that it has been randomly generated.                  

 http://www.btinternet.com/          www.gettyimages.com                                                               

Mariana Paz Castellanos, Rodrigo Langarica Ávila

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