CS30 -- Introduction to Computer Science II
Fall, 2006
Project 2: Mandelbrot Set
Deliverable 1

(updated 11/27/2006)


This is the first installment of your second project.  My intent is that this second project is much more modest than the MazeWar project.  Although it may be less fun as well, there are several interesting facets of the project that may make it interesting for you.  Do not wait until the last minute to work on the project deliverables.  You will suffer in many ways if you do.  The first deliverable is due Thursday Nov. 30 at 8:00am.  This is an individual project.  As always, I encourage you to talk to your peers or to me and to ask questions.  But the code you submit must be your own code.

The second project, once implemented, will display a rendering of the Mandelbrot Set for a given region of the complex plane.  We'll go over the math in class.  You can learn much more than you need for the project at the Wikipedia site for the Mandelbrot Set.  The Wikipedia page has pseudocode that take you most of the way.

Deliverable 2.1  Draw the Mandelbrot Set in two colors

Determining set membership.  Write a function, "inMandelbrotHuh(Point2D.Double)", that consumes a java.awt.Point2D.Double and returns a boolean value.  The truth value determines if the given point belongs to the Mandelbrot set (true) or not (false).  Note, the Point2D.Double is a point on the complex plane but corresponds to a pixel of your canvas that might be represented as a Point or a Point2D.  If you follow the pseudocode found at the Wikipedia site you should be fine.  But spend some time trying to understand the pseudocode -- we'll be going over it in class on Tuesday.  Update 11/27: Yes, you can copy the pseudocode and convert it to Java.  However, you may not share your code with your peers.

Display the image.  Display the points of the complex plane in the range [-2,1] to [1,-1].  Naturally, you'll need to map this region of the plane onto your canvas with upper-left corner [0,0] (actually, the appropriate value allowing for Insets) and a particular width and height.  You should code this mapping in a way that will allow maximal generality because next week you will be zooming in and out while recentering the portion of the plane that is visible on the canvas.  The resulting image should have two colors.  Points in the Mandelbrot set should be colored black, and other points should be colored a color of your choosing.

Progressive detail.  Your display code should render the picture in a manner that provides progressive detail.  That is, your code should break the region to be rendered into four rectangles and render those according to the mid-point of the rectangles.  But then each rectangle should be further subdivided into four rectangles and the process repeated.  This continues until the rectangle fits on a single pixel.  Update 11/27:  Your code should paint the canvas according to the membership of the center of the canvas, then divide the canvas into four regions and paint each region according to the membership of the respective midpoints of each region, and repeat this subdivision process until the region corresponds to a single pixel.  Furthermore, all of the regions at a given granularity should be painted before any of them are further painted at a finer granularity.

Packaging.  Wrap all this functionality in a "Mandelbrot" class, which extends Frame.  Include a main method that will display the image.  In your submitted code, use a canvas width and height of 600x400 and maximum iterations threshold of 100 -- you can play with these on your own and we will change them later.

Submission Instructions:
On your machine where you are doing your homework, create a folder called <your email name> followed by "P2.1".  For example, someone with email address "cjones" would create a folder called "cjonesP2.1".  Inside that folder, place whatever Java files are necessary for your Programming Projects in the same folder.  Finally, either tar or zip the folder so that when extracted, the folder "<emailname>P2.1" will be created.  Finally, submit via Eureka.