Overview / Logistics

The purpose of this lab is to get you practice with recursion with a fun application of drawing fractals, which are "infinitely self-similar shapes."" You can obtain the starter code with

git clone --recursive https://github.com/ursinus-cs174-s2023/Lab6_RecursiveDrawing.git

The code layout is based heavily on lab 3. You will be editing the file fractal.cpp. When you are finished, submit this file to canvas.

Learning Objectives

• Use recursion to implement complex behavior
• Use inheritance to share code between classes

Background: Fractals And Self-Similar Shapes

A fractal is a shape which is made up of smaller copies of itself. We'll be starting with something called the Sierpinski Triangle in this lab. The Sierpinski triangle is made up of 3 copies of itself. Let's say we were going to create a Sierpinski Triangle inside of these three points Δ abc:

Then, we'd find the midpoints d, e, and f of line segments ac, ab, and bc, respectively. We would then create the smaller triangles

• Δ aed
• Δ ebf
• Δ dfc

to get this image

If we continue this process recursively for each of the three new triangles, we get this

And if we continue this process recursively on each of the new triangles we get forever, we get the Sierpinski triangle! Below is the kind of image you will make by designing such a recursive function:

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Programming Task: Drawing The Sierpinski Triangle (3 Points)

I've started you off with the Point and LineSegment classes from lab 3. I added an additional method getMidpoint() to the LineSegment class, which should help with this lab.

Your Task: Complete an implementation of the drawSierpinski method in fractal.cpp. To test this, you can run the program sierpinski defined in sierpinski.cpp

As an example, running

should yield this image

and calling

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Extra Credit: Drawing The Koch Curve (+1 Point)

The Koch curve is a recursively defined curve that starts with a line segment and subdivides it as follows:

Repeating this process will yield the following curve:

Your Task

Fill in the drawKoch method in fractal.cpp. You can test this with the koch program defined in koch.cpp