MAT 2170: Laboratory 8
Key Concepts
1. Developing algorithms
2. Writing and using methods
Instructions
•Complete the Prelab (found at the back of this handout) before lab on Thursday.
•Staple your completed Prelab to the front of your printouts to turn in next week at the beginning
of lab 9.
Exercises
1. (Page 172, Exercise 5, SliderProgram:Bullseye) Rewrite the original Target program to uti-
lize the createFilledCircle() method. Get the number of circles to be drawn from the slider,
with a range from 1 to 15. Be sure to include and use the constants OUTER RADIUS and IN-
NER RADIUS, and follow all instructions in the exercise. There is no need to use a pause in this
program — the finished image is the goal. (Note: the slider program has been updated on the course
web site. If you are having trouble with re–running a slider program on your web site, please replace
the slider program for that project with the newer version, then replace the jar file.)
2. (Page 175, Exercise 11, Dialog Program: PrimeSolver) Create and test the isPrime() predicate
method, then extend this exercise to ask the user for a range, low to high, and determine all the
prime numbers in that range. These prime numbers are to be listed in a single dialog box.
3. (Julia Sets,DualSliderProgram:JuliaSet) You are to complete a program which produces a
graphical display of a fractal, or Mandelbrot set. A fractal is a function that maps coordinates to
values which we may then use to represent various colors. The method which will do this mapping,
JuliaColor(), is provided for you. The graphics window is to be divided into rows and columns
in the same way we created a checker board and other tilings of the graphics window. In this case,
however, instead of alternating block colors, the JuliaColor() method is used to determine the
color for each block.
In addition to completing the run() method, you must also complete the BlockCorner() and
ScreenToWorld() methods. BlockCorner(), when given the row and column of a block, is to
return the position of the block at the intersection of row and column. ScreenToWorld() is to
calculate the world region coordinate associated with the current block’s position in order to find
the corresponding Julia color.
How It Works
To every point (a, b) in the plane we can associate a function of two variables referred to as the
Julia map for (a, b), denoted by Fa,b and described by the formula
Fa,b(x, y) = (x2−y2+a, 2xy +b).
The Julia set for (a, b), denoted by Ja,b, is the collection of all points in the plane from which you
can start and never get too far away from the origin by repeated iterations of Fa,b. These sets turn
out to be bizarre fractal sets. Different choices of (a, b) often give rise to quite exotic sets Ja,b.
