Programming Assignment 8 (Toothpick Sequence)

Toothpick Sequence

In this programming assignment, you will develop a Python program to draw the "Toothpick" sequence (Wikipedia). You shall use the graphics.py package from Zelle's textbook available at Simple Graphics Library to solve this problem.

The sequence begins with one toothpick (iteration 0) placed on a canvas vertically as shown below:

In subsequent iterations, new toothpicks are placed perpendicular to open ends of previous toothpicks with the midpoint of the new toothpick placed touching the open end. Some toothpick arrangements, after 1, 2, 3, 4, and 8 iterations:

Here are two more arrangements (after 24 and 32 iterations):

The tricky part of the problem is to identify open ends that allow new toothpicks to be placed at that end. It is not always that the two ends of the new toothpick are open (sometimes they coincide with open end of another toothpick at the end of an iteration), in which case we should not place the new toothpick at such ends. The graphics.py package does not allow us to detect such coinciding ends, however since the graphics window, GraphWin, is a sub-class of TKinter Canvas class, we should be able to use some of the methods in the TKinter Canvas class to detect such ends.

The program should take the number of iterations as a command line input. The program should pop open a Canvas Window and draw the toothpicks for the number of iterations specified. It should then wait for a mouse click to terminate. It should also print to terminal the iteration #, #toothpicks added in each iteration, as well as the total number of toothpicks added after each iteration as shown in the output below.

Mac-mini:p8-toothpick raj$ python3 Toothpick.py 8
Iteration#: 1 #Toothpicks added in this iteration: 2 Total #toothpicks= 3
Iteration#: 2 #Toothpicks added in this iteration: 4 Total #toothpicks= 7
Iteration#: 3 #Toothpicks added in this iteration: 4 Total #toothpicks= 11
Iteration#: 4 #Toothpicks added in this iteration: 4 Total #toothpicks= 15
Iteration#: 5 #Toothpicks added in this iteration: 8 Total #toothpicks= 23
Iteration#: 6 #Toothpicks added in this iteration: 12 Total #toothpicks= 35
Iteration#: 7 #Toothpicks added in this iteration: 8 Total #toothpicks= 43
Iteration#: 8 #Toothpicks added in this iteration: 4 Total #toothpicks= 47
Mac-mini:p8-toothpick raj$