Homework 2

Due: Wednesday 8 February

The reading for this assignment is Chapters 4-6 of How to think....

Encapsulation and Generalization

  1. We have already seen two ways to draw a square. Here is a third:

    bob = Turtle(world)
    for i in range(4):
        fd(bob, 90)
    Create a file named polygon.py and type in this code. Run it and confirm that it draws a square[*].

  2. Encapsulate this code in a function called square and write a line of code that invokes it. HINT: when you change your program, you should be able to run the new version without restarting World.py.

  3. Generalize the function so that it takes a turtle and a distance, dist, as parameters.

  4. Generalize the function so that it takes an additional parameter, n, and draws an n-sided regular polygon. Hint: the angles of an n-sided regular polygon are $360 / n$ degrees. You might want to change the name of the function to polygon.

  5. Write a function called circle that takes a turtle, t, and radius, r, as parameters and that draws an approximate circle by invoking polygon with an appropriate distance and number of sides. Test your function with a range of values of r.

    Hint: figure out the circumference of the circle and make sure that dist * n = circumference.

  6. Make a more general version of circle called arc that takes an additional parameter theta, which determines what fraction of a circle to draw. theta is in units of degrees, so when theta=360, arc should draw a complete circle.

  7. Chances are that when you started to write arc you realized that you weren't able to reuse polygon, even though arc and polygon are very similar. Maybe you ended up doing ``design by copy and paste.'' If so, then you end up with two very similar chunks of code; if you want to make changes later, you will find yourself making every change twice.

    Refactor the program so that arc, circle, and polygon all invoke a single (very general) function.

  8. Write an appropriately general function called flower that can draw flowers like this:


  9. As usual, you should look over your code to see if there are opportunities to make it better, and add comments that explain what each function does, and that explain anything that is not obvious. Add a comment at the beginning that has your name in it. Print a copy of the code and, if you make a flower you are proud of, a copy of the output (by hitting Print Canvas and then typing lpr canvas.eps).


  1. Download and run Wanderer.py:

    wget http://wb/sd/code/Wanderer.py
    python Wanderer.py
    Print a copy of the code (a2ps -1 Wanderer.py) and read it over. It uses some features we haven't studied yet, but you should be able to understand enough to modify it.

  2. The distance function is not implemented correctly. You should change it so that it actually computes the distance from the given turtle, self, to the origin.

  3. One problem with Wanderers is that they eventually go off the screen, and they usually don't come back. One way you might try to solve this problem is to modify step so that if a Wanderer is too far from the origin, it turns around.

    Make this change and run the program again. Does it work? (You might want to draw a circle at the appropriate radius).

  4. Think of a way to keep the Wanderers in bounds. Ideally your algorithm should be simple (easy to implement), effective (it should keep the Wanderers in bounds), and gentle (it shouldn't cause the Wanderers to behave too erratically near the boundary).

  5. Prepare and print your code as usual.

More fun

The following exercises are optional. You don't have to turn them in, but if you do something cool, I would be happy to see it.

  1. Modify step so that Wanderers ``orbit;'' that is, so they try to stay the same distance from the origin.

  2. Modify step so that Wanderers interact with each other. For example, you could have them run after each other, or avoid each other, or bounce off each other when they collide. World objects have an attribute called animals that is a list of the animals that are currently in the world.

  3. Create different kinds of Turtles (not just Wanderers) that have different definitions of step. You could have one kind that runs after other turtles, and another kind that runs away.

  4. Make Turtles behave like a paintbrush.

    1. Add a Turtle attribute named thickness that controls the thickness of the line.

    2. Modify World.py so that when a Turtle moves, the thickness of the line is the turtle's thickness.

    3. Modify step so that it reduces the thickness each time the turtle moves.

    4. Write a function called dip that resets the thickness.

    5. Add a dip button to the Turtle Control Panel

    6. Use Turtles to make calligraphy.


... square[*]
You might find it helpful to put your code in a file named turtle_code.py, because that's what World.py runs by default. But when you are done, please put your solution in polygon.py.