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1.Choose your favorite positive integer A between 1 and 100 2.If A = 1, then STOP 3.If A is even, replace A by A/2 and go to step 2 4.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. The Mathematical Kevin Bacon Game

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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

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What you should know after today You should be able to explain what a feedback system is You have a 1 st idea of what Chaos means and how Chaos makes simulation on Computers difficult

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What is a feedback system? XnXn function X n+1

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Can Fractals Really Arise Naturally?

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Fractals – The Geometry of Feedback Systems

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An Example Feedback System Growth Rate Should be proportional to this 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

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MWHAHAHAHAHA!

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So Whats 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

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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?

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