Week 2, Problem 3: Python Bonsai
[30 points + 15 points (extra); individual or pair] filename: hw2pr3.py

This problem asks you to create two classic kinds of recursive images: a spiral and a tree made of line segments (and optionally the Koch Snowflake). If you are so inclined, you can make your tree more realistic than just a stick tree and get extra credit.

On a typical computer, the turtle drawing module is installed and ready to use. (If for some reason your computer doesn't have turtle installed, then you can use the csturtle module instead. To learn more about how to get csturtle, go here.)

To learn how to use turtle and to see all of it's commands, click here.

Note: When you run a program with turtle commands, a special window will open where the drawing will take place (This window may "hide," appearing BEHIND the other windows). If you run the program again, that same window will be used again. However, when you want to finally close that drawing window, you must first type done() at the IDLE prompt. Then you can close the window (for example, by clicking on the red circle at the top left of the window on a Mac).

To simplify grading, please be sure to name your functions as specified in these problems... . The graders thank you!!

Part 1

Write a function

spiral( initialLength, angle, multiplier )

that uses the csturtle drawing functions to create a spiral that has its first segment of length initialLength and whose neighboring segments form angles of angle degrees. The multiplier will be a float that will indicate how each segment changes in size from the previous one. For example, with a multiplier of 0.5 each side in the spiral should be half the length of the previous side.

The spiral should stop drawing when it has reached a side length of less than 1 pixel or greater than 1000 pixels... .

Part 2

"The fallen tree" the idea here is to create a function that draws the side-view of a tree:

svTree( trunkLength, levels )

Here is an example of the output from my function when svTree( 128, 6 ) is run:

and another example of the output when svTree( 50, 2 ) is run:

Note that these are really side view! Of course, calling left(90) before the call to svTree will yield a more traditional pose... .

The key thing to notice about both of these pictures is that the pen is back at the start (root) of the tree at the end of the function call! This is the key to all happiness when specifying recursive images!

One thing not to worry about is the number of branches (anything greater than 1 is OK), the exact angle of branching, the reduction of the trunkLength in sub-branches, etc. Design your own tree by making aesthetic choices for each of these.

Submission

You should submit your hw2pr3.py file at the Canvas.

Not enough? Extra credit options...

Choice 1: Your own recursive designs...

[15 points, individual or pair]

For extra credit of up to 5 points, feel free to design and implement your own recursive artwork. One starting point might be "sprucing up" your svTree function further by adding other cool features. We're "pining" for some interesting variants. If you do add extra features to your tree -- or create any other work -- make sure to "fir"nish us with a comment at the very top of your code indicating what you did and how to invoke your function.

Consider using the fill and color settings or changing the theme away from trees completely. The CS turtle reference page provides documentation for the functions available from the turtle module. See the description of a function name on that page.

Choice 2: The Koch curve

[15 points, individual or pair]

A more focused task for an additional possible 5 points extra credit is to create a function named

snowflake(sideLength, levels)

The idea is that snowflake will draw levels recursive levels of the Koch Snowflake, a fractal curve that is described here, among other places on the web. Basically, a Koch snowflake of level 0 is simply an equilateral triangle with side length equal to sideLength. Each increment of level replaces the middle third of all of the snowflake's sides with a "bump" that is, itself, a smaller equilateral triangle.

One hint that may or may not be helpful to you is that in our solution, we write a helper function called snowflakeSide( sideLength, levels ) that draws just one side of the underlying equilateral triangle. Then, the snowflake function was quite similar to the tri() example from class. The key recursion occurs in snowflakeSide. This division of labor is not required, however - there are a number of alternative ways to organize it.

Here are four steps of the Koch curve's progression:

Submission

You should submit your hw2pr3.py file at the Canvas.