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• CS167-C, 2016F
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• Homework 6

Homework 6: Plotting Functions

Assigned

Wednesday September 21, 2016

Due

noon, Friday September 23, 2016

Summary

The goal of this assignment is to get more experience with functions, loops, and using turtles.

Collaboration

Do this assignment with your assigned partner.

Submitting

Submit a Python program using the online turnin form. See below.

Scoring

12 points

Assignment

Create a file named turtleplot.py in which you will write your code. Write the following functions:

Part 1. Sums of series

Write the following functions:

• identity(x) returns x.
• square(x) returns the square of x.
• sum_to_n(n) returns the sum 1 + 2 + … + n, calculated using a for loop.
• sum_odds(n) returns the sum 1 + 3 + 5 + … + K_n, where K_n is the n^th odd number, calculated using a for loop.
• sum_frac(n) returns the sum 6/1 + 6/2 + 6/4 + 6/8 + 6/16 + … + 6/2ⁿ, calculated using a for loop.

Part 2. Plotting with a turtle

Write a function tplot(tortoise, f) that takes as parameters a turtle and a function, and uses the turtle to plot the function.

Here's an algorithm outline:

• Use a for loop to iterate over x values from 1 to 40. (Why not 0?)
• For each value of x, call the given function to compute the value y = f(x).
• Tell the turtle to go to the location (x,y) and draw a dot. (See the Turtle module documentation if you're not familiar with the goto and dot methods.)
  

Part 3. Writing a main function

Write a main function with the following code. Remember to import the turtle module at the top of your file.

def main():
    turtle.setworldcoordinates(0, -20, 40, 80)
    plotter = turtle.Turtle()
    plotter.speed(0)
    plotter.penup()
    tplot(plotter, square)
    screen = plotter.getscreen()
    screen.exitonclick()

If your tplot function is working, you should see Plotter the turtle plotting the points of the square function:

Try plotting the other functions as well by changing the argument to tplot from square to another function.

You can also pass in built-in functions from math, for example passing math.sin looks like this:

Part 4. Comparing functions

Modify the main function so that it plots several functions in different colors as follows:

Above & beyond

• Figure out how to neatly draw lines between the dots.
  
• Make an interesting design by plotting some other functions than the ones suggested.

Submitting your work

Submit one file, turtleplot.py, using the turnin form.

Point distribution

• Style and following guidelines - 1 pt
• identity, square - 1 pt
• sum_to_n and sum_odds - 3 pts
• sum_frac - 2 points
• tplot function - 3 pts
• main function and comparing plots - 2 points