Sierpinski
CSSE 221 – Fundamentals of Software Development Honors
Fall 2008–2009

Work on this exercise individually. Get help only from your instructor or student assistants -- that will maximize your learning experience on this project.

Goals

The goals of this exercise are to apply and hence reinforce your understanding of:

• Recursion

Overview

You will write the recursive method of a project that displays Sierpinski triangles like these:

					Link to Sierpinski level 5 picture
Level of detail:	0	1	2	3	5

We supply all of the project except the implementation of the recursive method drawSierpinski -- you will write that method, per the instructions below.

Instructions

1. In Eclipse, checkout the Sierpinski project from your individual repository.
2. Run the project. You should see a single triangle (the Sierpinski triangle whose level of detail is zero). Pressing the buttons has no effect (yet), because you have not implemented the drawSierpinski method (yet -- see next step of instructions).
3. Read ALL of this step of the instructions before doing any of this step.

   Complete the project by doing ONLY the following -- NO OTHER CHANGES ARE PERMITTED (e.g. NO ADDITIONAL FIELDS):

   1. Add parameters as needed to the drawSierpinski method in SierpinskiPanel.
      • Keep the two parameters that drawSierpinski already has -- you will need to add more parameters for the method to become recursive.
   2. Change the call to drawSierpinski at lines 69-70 of SierpinskiPanel to have whatever additional arguments it needs.
      • Keep the two existing arguments.
   3. Write the code for drawSierpinski -- it MUST be recursive (else no credit).

   You may find the following geometric/graphical facts helpful (READ CAREFULLY):

   • Draw only the BLACK triangles -- that creates the desired effect since the supplied code supplies a blue, background triangle.
   • Suppose that you have a big, right-side-up, blue triangle (per the diagram below on the left). Suppose that you want to inscribe an upside-down, black triangle (to yield the diagram below on the right).

     Let (X, Y) denote the coordinate of the top point of the big, right-side-up, blue triangle. Let L denote the length of a side of the big, right-side-up, blue triangle. Then (in the graphics coordinates that Java and other systems use, where the y-axis goes down, not up):

     • The leftmost point of the inscribed, upside-down, black triangle is:

       		[X - L/4, Y + (L * sqrt(3.0) / 4.0)]
       

     • The rightmost point of the inscribed, upside-down, black triangle is:

       		[X + L/4, Y + (L * sqrt(3.0) / 4.0)]
       

     • The bottommost point of the inscribed, upside-down, black triangle is:

       		[X, Y + (L * sqrt(3.0) / 2.0)]
       

4. Turn in your work by commiting your project to your individual repository.