Programming Assignment Checklist: Recursive Graphics

Frequently Asked Questions

What preparation do I need before beginning this assignment? Read Sections 2.1–2.3 of the textbook.

What is the layout of the initial equilateral triangle? By using the definition in the assignment and the Pythagorean theorem, you can prove that the top vertex lies at (1/2, √3/2). We illustrate the coordinates of the initial iterations below to help you double-check.

How do I draw a filled equilateral triangle? Use StdDraw.filledPolygon() with appropriate parameters.

May I use a different color from black to fill in the triangles? Yes, you may use any color that contrasts with the white background.

How can I create colors that aren't predefined in standard drawing? It requires using objects that we'll learn about in Chapter 3. In the meantime, you can use this color guide.

How should I go about doing the artistic part of the assignment? This part is meant to be fun, but here are some guidelines in case you're not so artistic. A very good approach is to first choose a self-referential pattern as a target output. Check out the graphics exercises in Section 2.3. Here are some of our favorite student submissions from Fall '10. See also the Famous Fractals in Fractals Unleashed for some ideas. Here is a list of fractals, by Hausdorff dimension. Some pictures are harder to generate than others (and some require trig); consult a preceptor for advice if you're unsure.

What will cause me to lose points on the artistic part? We will deduct points if the code to generate your picture is too similar to Htree, Sierpinski or Brownian. Are the shapes overlapping in an interesting order? Or, does the signature of your recursive method include a novel argument? Cosmetic changes like changing colors or changing shapes to triangles are not a bad idea, but it's more important that your program exhibits a different recursive behaviour.

Example: the Quadricross looks very different from the in-class examples, but the code to generate it looks extremely similar to HTree, so it is a bad choice. Non-example: Even though the Sierpinski Curve eventually generates something that looks identical to the Sierpinski Triangle, the code is very different and so it would earn full marks.

You will also lose points if your artwork can be created just as easily without recursion (like Factorial for example). If the recursive call tree for your function is a straight line, it probably falls under this category.

May I use .gif, .jpg, or .png in my artistic creation? Yes. If so, be sure to submit them along with your other files. Make it clear in your readme.txt what part of the design is yours and what part is borrowed from the image file.

My function for Art.java takes several parameters, but the assignment says that I can only read in one command-line argument N. What should I do? Choose a few of the best parameter values and do something like the following:

if      (N == 1) { x = 0.55; y = 0.75; n = 3; }
else if (N == 2) { x = 0.55; y = 0.75; n = 5; }
else if (N == 3) { x = 0.32; y = 0.71; n = 8; }
else if ...

Possible Progress Steps

These are purely suggestions for how you might make progress. You do not have to follow these steps. Note that your final Sierpinski.java program should not be very long (no longer than Htree, not including comments and blank lines).

• Review Htree.java from the textbook and lecture.

• Write a (nonrecursive) function filledTriangle() that takes three real-valued arguments (x, y, and size), and draws a filled equilateral triangle (pointed downward) with bottom vertex at (x, y) and side length size. To debug and test your function, write main() so that it calls filledTriangle() a few times, with different parameters. You will be able to use this function without modification in Sierpinski.java.

• Write a recursive function sierpinski() that takes 4 arguments (n, x, y, and size) and plots a Sierpinski triangle of order n, whose largest triangle has side length size and bottom vertex (x, y).

  • Write a recursive function sierpinski() that takes one argument n, prints the value n, and then calls itself three times with the value n-1. The recursion should stop when n becomes 0. To test this function out, write main() so that it reads one integer N from the command line and calls sierpinski(N). Excepting the spacing, you should get the following output when you call sierpinski() with N ranging from 0 to 5. Make sure you understand how this function works, and why it prints the numbers in the order it does.

  • Modify sierpinski() so that in addition to printing n, it also prints the size of the triangle to be plotted. Your function should now take two arguments: n and size. The initial call from main() should be to sierpinski(N, 0.5) since the largest triangle has side length 0.5. Each successive level of recursion halves the length. Your function should produce the following output.

  • Modify sierpinski() so that it takes 4 arguments (n, x, y, and size) and plots a Sierpinski triangle of order n, whose largest triangle has side length size and bottom vertex (x, y). Start by drawing Sierpinski triangles with pencil and paper. Use the picture in the Q+A above to figure out the geometry of where the smaller Sierpinski triangles should go.

  • Remove all print statements before submitting.

Reviewing Your Program

• Your Art.java program must take exactly one integer command-line argument N (which will be between 1 and 7).

• Don't call StdDraw.save(), StdDraw.setCanvas(), or StdDraw.setXscale() (or Y). These interfere with grading.

• Be sure to include a comment just above each method definition explaining what the method does — this will be required in all future assignments as well. Leaving a comment for main is not required since the header already does basically the same thing.

• Continue to follow the guidelines from previous weeks.

Challenge for the bored

Consider using our StdDraw3D library instead of StdDraw to create a three-dimensional fractal design! (Note: This is not for extra credit nor for submission.) You can find documentation on the booksite.

To check that you have downloaded StdDraw3D when running the installer, go to the command prompt and type:

java StdDraw3D

Enrichment

• Here's a fractal in polymer clay, a fractal cookie, a fractal pizza, a fractal hamantaschen, and puff pastry.