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40 lines
1.5 KiB
Text
40 lines
1.5 KiB
Text
#import "./common/common.typ" : *
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#show: template
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= Week 10
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== Exercise 1.3.45
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_Chaos_. Write a program to study the following simple model for population growth, which might be applied to study fish in a pond, bacteria in a test tube,
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or any of a host of similar situations. We suppose that the population ranges from
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$0$ (extinct) to $1$ (maximum population that can be sustained). If the population at
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time $t$ is $x$, then we suppose the population at time $t + 1$ to be $r x (1-x)$, where the
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argument r, known as the _fecundity parameter_, controls the rate of growth. Start
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with a small population—say, $x = 0.01$—and study the result of iterating the model, for various values of $r$. For which values of $r$ does the population stabilize at
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$x = 1 - 1/r$ ? Can you say anything about the population when $r$ is $3.5$? $3.8$? $5$?
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#table(
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columns: 3,
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$3.5$,
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$3.8$,
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$5$,
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$2$,
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[Oscillation between 4 values],
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[Sustained chaos],
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[Dies from overpopulation in 5 ticks],
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[Sustained $1-1/r$]
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)
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== Exercise 1.4.26
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_Music shuffling_. You set your music player to shuffle mode. It plays each of
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the n songs before repeating any. Write a program to estimate the likelihood that
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you will not hear any sequential pair of songs (that is, song 3 does not follow song
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2, song 10 does not follow song 9, and so on).
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== Exercise 1.5.32
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_Clock_. Write a program that displays an animation of the second, minute,
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and hour hands of an analog clock. Use the method `StdDraw.pause(1000)` to
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update the display roughly once per second.
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