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Fractals in Real Life


Date: 10/04/1999 at 09:09:21
From: Kristin Argotsinger
Subject: The use of fractals in real world life.

How are fractals used by scientists and mathemeticians in the real 
world today?

I know what a fractal is and have a good amount of background 
information on them, but I can not think of how they are used in the 
real world today.

Thank you for your time!

Kristin Argotsinger


Date: 10/05/1999 at 21:48:28
From: Doctor Douglas
Subject: Re: The use of fractals in real world life.

Hi Kristin,

This is a great question! As you know, fractals describe geometrical
objects that have more and more sub-structure as one views them at
higher and higher magnifications. An excerpt from the sci.nonlinear 
FAQ at

  http://amath.colorado.edu/appm/faculty/jdm/faq.html   

says that

  "Fractals also approximately describe many real-world objects, such   
   as clouds, mountains, turbulence, coastlines, roots and branches of 
   trees and veins and lungs of animals."

Scientists and engineers and mathematicians and other people 
interested in these objects (such as a computer graphics person 
working to create an image of an artificial landscape) might use 
fractals in their work. For example, a biomedical engineer might want 
to calculate how much surface area covers the bronchial tubes within a 
human lung. Or maybe an environmentalist wants to estimate how many 
miles of coastline could be affected by a large oil spill. These are 
ways that scientists use fractals to describe or approximate the 
*structure* of a real (or imagined) object.

Another way scientists and mathematicians sometimes use fractals 
is in the field of nonlinear dynamics, where the behavior of a system 
is *described* by a geometrical object in something called "phase 
space."  This object can assume many different forms, such as points 
or loops (circles, polygons, squashed ellipses, etc.). Points indicate 
the situation when there is no change in behavior, while loops 
describe when a system does the same thing over and over again 
continuously, (i.e. it "oscillates"). An example of another shape is a 
spiral. Dynamicists use the spiral to describe how a pendulum swings 
back and forth and gradually spirals into the origin as time goes on.  

As for fractals, there are some behaviors (often called "chaotic") 
that are so complex that the geometric object is a fractal, rather 
than a simpler shape. A cardiologist might monitor a patient's 
heartbeat and chart its behavior over time. A healthy patient might 
have a slightly irregular heartbeat, and this might be visible in the 
record as a fractal. But if the heartbeat becomes too regular, the 
fractal might morph into a simpler shape, such as a loop, indicating 
that the patient might be at risk for a heart attack. In this example 
the fractal is used to help the physician monitor the status of her 
patient.

So you see that fractals can be used to describe the *structure* of 
things in the real world, or the *behavior* of systems in time.

Hope this helps.  If anything in this response is confusing to you, 
please don't hesitate to write back. For more information, you might 
wish to visit the nonlinear FAQ (URL above) or the fractal FAQ at

  ftp://rtfm.mit.edu/pub/usenet/news.answers/fractal-faq   

Good luck!

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Fractals

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