Homework 6



Homework 6: Due Friday 8 February

Please hand in all work on separate paper -- please don't hand in your work on the photocopied worksheets.

Computer Exercises

For these problems you'll want to use the three computer programs located at http://hornacek.coa.edu/dave/Chaos.

For each r value, do the following.

  1. Determine the long-term behavior of the orbits. Are the orbits periodic (what period?) or chaotic?
  2. Does the equation show the butterfly effect?
Sketch or print out any graphs you use to draw your conclusions.
  1. 3.4
  2. 3.7
  3. 3.835
  4. 3.5699456718695445 (don't round off).

Lesson 7: The Butterfly Effect (I haven't given you this sheet yet. I'll bring them to class, and also put a pile outside my door in case you want one before Thursday.

  1. 2.

Lesson 2: Fractals Generated by Removals

  1. 1-4. Also, find the dimension for each object.
Lesson 3: Self-Similarity
  1. 1-5. Also, find the dimension for each object.
Lesson 9: Fractal Dimension
  • No problems from this section. However, if you're confused about this dimension stuff that we've been doing in class, you might want to look at pp. 132-134; there's a nice explanation of dimension here.

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