Homework 2: Mandelbrot Set


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Homework 2: Mandelbrot Set

Problem Description
Input specification
Output specification
Final Notes
This assignment helps you get familiar with:
1. Pthread
2. Hybrid parallelism (MPI + OpenMP)
3. Load balancing techinques
In this assignment, you are asked to parallelize the sequential Mandelbrot Set program using:
1. (hw2a) – pthread / std::thread
2. (hw2b) – MPI + OpenMP
Problem Description
Mandelbrot Set is a set of complex numbers that are quasi-stable when computed by iterating the
is some complex number:
is the iteration of the complex number
if for any , belongs to Mandelbrot Set
What exactly is Mandelbrot Set?
It is fractal: An object that display self-similarity at various scale; Magnifying a fractal reveals
small-scale details similar to the larger-scale characteristics
After plotting the Mandelbrot Set determined by thousands of iterations:
= C
= Zk
2−1 + C
C C = a + bi
Zk+1 (k + 1)th
|Zk | ≤ 2 k C
You can get a felling about Mandelbrot Set at
In this homework, you are asked to implement 2 versions:
1. hw2a – thread version, using Pthread or std::thread.
2. hw2b – hybrid version, using OpenMP and MPI.
Both versions follow the same input & output format.
Input specification
The input is specified from the command line. Ther are no input files.
Your program should accept the following srun command:
srun -n$procs -c$threads ./executable $out $iters $x0 $x1 $y0 $y1 $w
For example, the image in Problem Description is created by:
srun -n1 -c1 ./hw2seq out.png 10000 -2 2 -2 2 800 800
The meaning of the arguments are:
$procs – int; [1, 48]; number of processes. Always 1 for the thread version (hw2a).
$threads – int; [1, 12]; number of threads per process.
$out (argv[1]) – string; the path to the output file.
$iters (argv[2]) – int; [1, ]; number of iterations. (the largest int is around
$x0 (argv[3]) – double; [-10, 10]; inclusive lower bound of the real axis.
$x1 (argv[4]) – double; [-10, 10]; non-inclusive upper bound of the real axis.
$y0 (argv[5]) – double; [-10, 10]; inclusive lower bound of the imag axis.
$y1 (argv[6]) – double; [-10, 10]; non-inclusive upper bound of the imag axis.
$w (argv[7]) – int; [1, 16000]; number of points in the x-axis for output.
$h (argv[8]) – int; [1, 16000]; number of points in the y-axis for output.
Output specification
Your programs should produce a PNG image at $out, visualizing the Mandelbrot Set in the given
We provide a sequential version to show how the pixels are rendered. See Resources.
1. Correctness (60%)
a. thread version (30%)
b. hybrid version (30%)
Several test cases will be used to test your implementations. You get 30 points for an
implementation if you passed all the test cases, points if there are failed test
For each test case, you pass it if:
Your implementation produced a valid PNG image.
At least 99.6% of the pixels in your output are identical to the corresponding pixel produced
by the sequential version. You are advised not to use this tolerance for optimizations.
The execution time of your implementation is shorter than the execution time of the
sequential version + 30 seconds.
2. Performance (30%)
a. thread version (10%)
b. hybrid version (20%)
You need to pass all the correctness test cases in the corresponding version in order to get
performance points.
Points are given according to the relative performance of your program among all the students.
3. Demo (10%)
Each student is given 5 minutes to explain the implementation followed by some questions
from TA.
Points are given according to your understanding and explanation of your code, and your
answers of the TA questions.
2 × 10
2.1 × 10
(30 × 0.7 )
k k
Put your source code under at ~/homework/hw2 in apollo31:
Your Makefile – ~/homework/hw2/Makefile
Source code for thread version – ~/homework/hw2/ or
Source code for hybrid version – ~/homework/hw2/ or
make hw2a and make hw2b will be used to compile your code.
Use hw2a-judge and hw2b-judge to check and submit your code before the deadline. You can
submit as many times as you want.
Resources are given under /home/ipl19/x/hw2/:
Sequential version – hw2seq.c
Example Makefile – Makefile
(TODO) Testcases cases/
Submissions can be viewed at and
In order to compare your image with the the answer, use:
hw2-diff answer.png yourimg.png
Here are a few programs that be used to get the output PNG to your computer for display:
Final Notes
Contact TA via [email protected] or iLMS immediately if you find any problems with the
homework specification, judge scripts, example source code or the test cases.
You are allowed to discuss and exchange ideas with others, but you are required to write the code
on your own. You’ll got 0 points if we found you cheating.

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