Lab 11: Part 2A: Recursive Turtles

The turtle section of our quick-reference page has information about the available turtle and turtleBeads drawing commands.

The Turtle module API is the official Python documentation for the turtle module.

Setup

In the lab11 folder, open recursiveTurtles.py.

At the bottom of the starter file is a function run, which invokes setupTurtle. The invocations of the functions you write (e.g., row()) will go inside run(). This is how you will test your turtle functions today.

Task 1. The provided `square` function and how to test

def square(length):
    """Draws a square of size length maintains heading
       and position invariant"""
    for _ in range(4):
        fd(length)
        lt(90)

# WRITE YOUR FUNCTIONS HERE

...then invoke square in the run function.

How to test your functions:

Call your function from within the run function (near the bottom of your file)
Run your file in Thonny
This will automatically call the run function, which in turn will call your function.

Do a test run with square by calling square from within run.

Note that there is a test_recursiveTurtles.py file in your lab09 folder, but it does not include tests for all the functions and the tests rely on drawing lines in a certain order, which you do not necessarily have to follow. So, for today, it is better to test by calling your functions from within the run function.

Task 2: Row of squares

Partner A

Write a recursive method called row(number, size) that draws a horizontal row of number squares of size size.

This function must be recursive and maintain a position and heading invariant.

FYI: In the example screenshots below, the Turtle's pen was set to red ( via pencolor('red')), but your pen color will be black by default.

row(3, 50)
A row of three red squares, touching horizontally at their edges. The turtle is in the bottom-left facing to the right.

row(5,25)
A row of five smaller red squares, again with the turtle at the bottom-left and facing right.

Task 3: Spaced row of squares

Partner B

Write a recursive method called spacedRow(number, size) that draws a horizontal row of number squares of size size with a constant space of size/4 between each square.

This function must be recursive and maintain a position and heading invariant.

spacedRow(3,50)
Another row of three squares with the turtle at the bottom-left, but this time there are gaps between each pair of squares. The gaps are 1/4 as wide as the squares themselvs.

Another row of three squares with the turtle at the bottom-left, but this time there are gaps between each pair of squares. The gaps are 1/4 as wide as the squares themselvs.

spacedRow(5,25)
A row of 5 smaller squares with gaps between them.

Task 4: Decreasing row of squares

Partner A

Write a recursive method called decreasingRow(number,size) that draws a horizontal row of number squares. The first square has size size and each subsequent square is half the size of the previous one.

This function must be recursive and maintain a position and heading invariant.

decreasingRow(3,100)
Three squares placed horizontally edge-to-edge, where the second square is 1/2 as tall (and wide) as the first, and the third is half as tall/wide as the second (so 1/4 of the first square). The turtle is placed (you guessed it!) at the bottom-left of the first square, facing right. The bottoms of eqch square are aligned to form a straight line, while their tops step downwards.

Three squares placed horizontally edge-to-edge, where the second square is 1/2 as tall (and wide) as the first, and the third is half as tall/wide as the second (so 1/4 of the first square). The turtle is placed (you guessed it!) at the bottom-left of the first square, facing right. The bottoms of eqch square are aligned to form a straight line, while their tops step downwards.

decreasingRow(5,100)
A row of 5 squares of decreasing size, where each square is 1/2 as large as the previous one. The turtle is yet again placed at the lower-left corner and facing right.

A row of 5 squares of decreasing size, where each square is 1/2 as large as the previous one. The turtle is yet again placed at the lower-left corner and facing right.

Task 5: Nested squares

Partner B

Write a recursive method called nestedSquares(number,size) that draws number nested squares. The largest square has size size and each subsequent square is half the size of the previous one. The squares are anchored in the lower left corner.

This function must be recursive and maintain a position and heading invariant.

nestedSquares(3,90)
A series of three squares of decreasing sizes (each 1/2 as large as the previous) but this time their lower-left corners are on top of each other, so that the smaller squares are drawn within the larger squares. The turtle is at that lower-left corner, and is facing right.

A series of three squares of decreasing sizes (each 1/2 as large as the previous) but this time their lower-left corners are on top of each other, so that the smaller squares are drawn within the larger squares. The turtle is at that lower-left corner, and is facing right.

nestedSquares(5,130)
A series of 5 nested squares, each 1/2 as large as the previous square.

Task 6: Diagonal squares

Partner A

Write a recursive method called diagonal(number,size) that draws number decreasing diagonal squares. The largest square has size size and each subsequent square is half the size of the previous one.

This function must be recursive and maintain a position and heading invariant.

diagonal(1,100)
A single square of size 100, with the turtle at the bottom-left corner.

diagonal(2,100)
Two squares, the second half as large in each dimension as the first (so 1/4 the area). The second square's lower-left corner is touching the upper-right corner of the first square, so the second square appears diagonally up and to the right from the first square. The turtle remains at the lower-left corner of the first square.

Two squares, the second half as large in each dimension as the first (so 1/4 the area). The second square's lower-left corner is touching the upper-right corner of the first square, so the second square appears diagonally up and to the right from the first square. The turtle remains at the lower-left corner of the first square.

diagonal(3,100)
Three diagonal squares, each half the dimension of the previous, stacked diagonally corner-to-corner, so that the second square is touching the first square's upper-right corner with its lower-left corner, and the third square has that same relationship with the second square.

Three diagonal squares, each half the dimension of the previous, stacked diagonally corner-to-corner, so that the second square is touching the first square's upper-right corner with its lower-left corner, and the third square has that same relationship with the second square.

Task 7: Double Diagonal squares

Partner B

Write a recursive method called doubleDiagonal(number,size) that draws number decreasing diagonal squares. The largest square has size size and each subsequent square is half the size of the previous one. Each recursive call draws two new squares: one anchored at the upper right corner and the other anchored at the lower left corner.

This function must be recursive and maintain a position and heading invariant.

doubleDiagonal(1,100) doubleDiagonal(2,100)

doubleDiagonal(3,100) doubleDiagonal(4,100)

Task 8: Super diagonal squares

Partner A

Write a recursive method called superDiagonal(number,size) that draws number decreasing diagonal squares. The largest square has size size and each subsequent square is half the size of the previous one. In superDiagonal, squares are placed on the diagonal at both the upper right corner and the lower left corner. Note: superDiagonal will not invoke diagonal.

This function must be recursive and maintain a position and heading invariant.

superDiagonal(1,125) superDiagonal(2,125)

superDiagonal(3,125) superDiagonal(4,125)