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Choose your favorite positive integer A between 1 and 100 If A = 1, then STOP PowerPoint Presentation
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Choose your favorite positive integer A between 1 and 100 If A = 1, then STOP - PowerPoint PPT Presentation


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The Mathematical Kevin Bacon Game. Choose your favorite positive integer A between 1 and 100 If A = 1, then STOP If A is even, replace A by A/2 and go to step 2 If A is odd, replace A by 3A + 1 and go to step 2

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Presentation Transcript
slide1

The Mathematical Kevin Bacon Game

  • Choose your favorite positive integer A between 1 and 100
  • If A = 1, then STOP
  • If A is even, replace A by A/2 and go to step 2
  • If A is odd, replace A by 3A + 1 and go to step 2

Count How Many Steps it takes. Your goal is to find the A that gives you the biggest number of steps.

fractals part 2 the geometry of feedback

Fractals (Part 2):The Geometry of Feedback

In which I speculate about a strange alternative-history for mathematics

But an initially rosy picture turns dark as the terrible clouds of Chaos loom on the horizon.

Chaos Warrior

what you should know after today
What you should know after today
  • You should be able to explain what a “feedback system” is
  • You have a 1st idea of what “Chaos” means and how Chaos makes simulation on Computers difficult
an example feedback system
An Example Feedback System

The environment can only support so many ninjas! Especially due to rampant destruction of natural ninja habitats.

Number of ninjas

Max ninjas the environment can support

Growth Rate

Should be proportional to this

so what s the deal with chaos
So What’s the Deal With Chaos?
  • Small deviations expand, so errors multiply
  • Eventually the noise overwhelms the signal
  • Because computers can only represent numbers with limited precision, they are very vulnerable to chaos
questions
Questions
  • What is an example of a feedback system?
  • Chaos has to do with errors multiplying. Since computers can add/subtract/multiply/divide perfectly, why is there a problem with chaos on computers?