HPC - Mandelbrot set

The file mpi-mandelbrot.c contains a MPI program that computes the Mandelbrot set; it is not a parallel program, because the master process does everything.

The program accepts the image height as an optional command-line parameter; the width is computed automatically to include the whole set. Process 0 writes the output image to the file mandebrot.ppm in PPM (Portable Pixmap) format. To convert the image, e.g., to PNG you can use the following command on the Linux server:

    convert mandelbrot.ppm mandelbrot.png

Write a parallel version where all MPI processes contribute to the computation. To do this, we can partition the image into \(P\) vertical blocks where \(P\) is the number of MPI processes, and let each process draws a portion of the image (see Figure 1).

Specifically, each process computes a portion of the image of size \(\mathit{xsize} \times (\mathit{ysize} / P)\) (see below how to handle the case where ysize is not an integer multiple of \(P\)). This is an embarrassingly parallel computation, since there is no need to communicate. At the end, the processes send their local result to the master using the MPI_Gather() function, so that the master can assemble the image. We use three bytes to encode the color of each pixel, so the MPI_Gather() operation will transfer blocks of \((3 \times \mathit{xsize} \times \mathit{ysize} / P)\) elements of type MPI_BYTE.

You can initially assume that ysize is an integer multiple of \(P\), and then relax this assumption, e.g., by letting process 0 take care of the last (ysize % P) rows. Alternatively, you can use blocks of different sizes and use MPI_Gatherv() to combine them.

You might want to keep the serial program as a reference. To check the correctness of the parallel implementation, compare the output images produced by the serial and parallel versions with the command:

    cmp file1 file2

They must be identical, i.e., the cmp program should print no message.

To compile:

    mpicc -std=c99 -Wall -Wpedantic mpi-mandelbrot.c -o mpi-mandelbrot

To execute:

    mpirun -n NPROC ./mpi-mandelbrot [ysize]

Example:

    mpirun -n 4 ./mpi-mandelbrot 800

Files

• mpi-mandelbrot.c