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Study Guides > Mathematics for the Liberal Arts

Discussion: Chaos

In the module we presented the Mandelbrot set, which can be generated with the following recursive relationship:

For some complex number c,

Z sub n plus 1 equals z sub n sup 2 plus c. Where z sub zero equals zero.

Recall that if this sequence always stays close to the origin (within 2 units), then the number c is part of the Mandelbrot Set. If the sequence gets far from the origin, then the number c is not part of the set.

The outcome of testing whether c is in the set is predictable. Some sequences exhibit behavior that is not predictable. For example, have you ever been frustrated that the weather report called for clear skies, and you were caught without a rain coat? Weather models are based on systems of equations that exhibit chaotic, or unpredictable behavior, making weather prediction a gamble.   For this discussion, find another example of a system that exhibits chaotic, unpredictable behavior.  Follow the rubric below to post your findings for the class. This assignment is required and worth up to 20 points.
Grading Criteria Points Possible
The system:
  • Is the system used to model real-life behavior?
  • What variables define the system?
  • Is it a unique system instead of a copy of a classmate's posting?
 5
The strategies:
  • What makes the system chaotic?
  • Are the variables correctly identified?
 5
The presentation:
  • Is the system explained well?
  • Is the explanation of what makes the system chaotic clear?
  • Are the appropriate terms used?
 4
Your responses:
  • Did you post at least two responses?
  • Did you explain how the examples helped you better understand chaos and chaotic systems?
  • Did you ask questions for clarification or make suggestions on how to change or improve the original application posting or any other follow-up postings?
 6