Lab 10: Turtles and Fractals

Due 11:59pm Tuesday, April 15, 2008

A skeleton version of the program will appear when you run update21 in a terminal window. The program handin21 will only submit files in this directory.

Some of the problems will have optional components that allow you to further practice your skills in Python. Optional portions will not be graded, but may be interesting for those wanting some extra challenges.

For this assignment you will write a program that implements a class of turtle objects. These are no ordinary turtles however as these turtles have a penchant for both the fine arts and computer science. These are turtles that can draw. Imagine placing a turtle on a canvas with a pen attached to his tail. This turtle can move forward and backward, turn right or left, and lift up or put down its tail. If the turtle moves while its tail is down, the pen leaves a trail behind the path of the turtle. You will write a class that allows you to create and manipulate drawing turtles. Then you will use this class to draw fractals.

A Turtle class
The current state of the turtle can be described by the following variables:

Begin by implementing the constructor and string methods:

To change or query the turtle's state, you can use a number of Turtle methods:

Testing the Turtle class
Turtle objects exist in a graphics window, whose center has the coordinates (0,0). When the turtle moves with its tail lowered, a line is drawn in the graphics window that tracks the turtle's movement. An example drawing is shown below for a turtle that initially starts facing East in the center of a 200x200 window.

Below is the code that was used to create this image:
  trevor = Turtle(200, 200)  # at (0,0) facing East
  trevor.left(90) # turn left 90 degrees (now facing North)

  # A triangle
  for i in range(3):
    trevor.forward(50)  # move forward 50 steps
    trevor.left(120)    # turn left 120 degrees

  trevor.up()           #stop drawing        
  trevor.goto(-80,-80)  #go to (-80, 80)
  trevor.down()         #resume drawing

  # A square
  for i in range(4):
    trevor.forward(40)  # move forward 40 steps
    trevor.right(90)    # turn right 90 degrees

  trevor.done()         # wait for mouse click to close window

You can also test your Turtle class with the drawHouse function that is included in the file. Be sure to test the Turtle class on these examples before implementing the fractals described below.

Koch curves
The textbook gives an example on page 465-466 of a fractal called the "Koch curve" that can be drawn recursively. You will write a function koch(turtle, length, degree) which draws a Koch curve of length length and degree degree. The koch function is not a method of the Turtle class.

The Koch curve is recursively defined:

Koch snowflakes

Write a function snowflake(turtle, sides, length, degree) that can draw a Koch snowflake, as described on page 465-466. A Koch snowflake is formed by putting together multiple copies of the Koch curve. The snowflake function is not a method of the Turtle class.

The algorithm for drawing a Koch snowflake with n sides is:

for each side:
  draw a Koch curve of the appropriate length and degree
  turn 360/n degrees
The snowflake shown below is an example of a Koch snowflake made with 3 Koch curves.

c-Curve Fractal

Write a function cCurve(turtle, length, degree) which draws a c-Curve, as described on page 466-467. See the text for an example picture. The cCurve function is not a method of the Turtle class.

C-curves are defined recursively:

Optional Components
You may include any additional methods in your class. Some of these methods can make writing other methods easier or extend the feature of you class. As noted above, these questions are NOT required to receive full credit. Furthmore, do not attempt to solve these problems until the required portion of the assignment is complete. There are many extensions you could add to this program. Here are a few we thought might be interesting.

Once you are satisfied with your program, hand it in by typing handin21 in a terminal window.