Mandelbrot Set in Scala
Download mandelbrot.scala.
Sequential version
Complete the compute method in the Row class.
It should generate a series complex numbers
real=(xStart+i*dx), imaginary=y
where i is a value between 0 (inclusive) and numPoints (exclusive).
Call each complex number C. For each value of C, determine how many times the equation
Z = Z*Z + C
can be iterated before the magnitude of some value of Z reaches 2, or the maxium number of iterations is reached.
The result of the compute method should be the list of iteration counts for each value of C.
To test, run the program:
scala mandelbrot.scala
It should produce output similar to the following:
0: List(1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
1: List(1, 1, 1, 2, 2, 2, 2, 2, 1, 1)
2: List(1, 1, 2, 3, 3, 3, 2, 2, 2, 1)
3: List(1, 3, 3, 4, 6, 18, 4, 2, 2, 2)
4: List(1, 3, 7, 7, 1000, 1000, 9, 3, 2, 2)
5: List(1, 1000, 1000, 1000, 1000, 1000, 7, 3, 2, 2)
6: List(1, 3, 7, 7, 1000, 1000, 9, 3, 2, 2)
7: List(1, 3, 3, 4, 6, 18, 4, 2, 2, 2)
8: List(1, 1, 2, 3, 3, 3, 2, 2, 2, 1)
9: List(1, 1, 1, 2, 2, 2, 2, 2, 1, 1)
Parallel version using actors
Use actors to compute each row in parallel.
Add the following imports to the top of the source file:
import scala.actors.Actor
import scala.actors.Actor._
Suggested approach: define a RowActor class:
Then, define a Mandelbrot actor class. Its job should be to create a RowActor for each row that needs to be computed, and send it one row as a message. It should receive messages for completed rows from the RowActors. When all rows are completed, it should print out all of the completed rows in order (similar to the original program output.)
You can change the code in the main function to something like the following:
val m = new Mandelbrot(x1, y1, x2, y2, cols, rows)
m.start()
m ! Compute
Here, we're assuming that the Mandelbrot actor accepts a Compute message that will start the computation. You can define this as a case object:
case object Compute
Hints
You may want to define a CompletedRow class, something like the following:
class CompletedRow(val rowNum : Int, val counts : List[Int]) {
}
A CompletedRow object represents the finished iteration counts for a particular row, along with the row number. This can be used as the type of message that RowActors send to the Mandelbrot actor.
The Mandelbrot actor can prepend (cons) each CompletedRow object to a list. When the list is complete, the CompletedRows can be sorted by row number.
