A Buddhabrot computed with co_sum() and saved in a PPM file

For the moment, this repository contains only one example (but you may also be interested by exploring_coarrays).

ppm_coarray_buddhabrot.f90 is a CLI program drawing a Buddhabrot in a portable pixmap binary format (PPM) file, a very basic uncompressed image file format. Each Fortran image is computing its own Buddhabrot, and they are finally summed using the co_sum() collective subroutine. The process is therefore very similar to what is done in astrophotography.

Compiling and executing

GFortran>=16.0

Starting from version 16, GFortran supports natively coarrays using shared memory mulithreading on single node machines:

$ gfortran -Ofast -march=native -mtune=native -fcoarray=lib ppm_coarray_buddhabrot.f90 -lcaf_shmem && ./a.out

You can force the number of images (8 for example) with:

$ export GFORTRAN_NUM_IMAGES=8

The -lcaf_shmem is necessary until a -fcoarray=shared option is added in a later GFortran release.

GFortran<16

You needed to install OpenCoarrays and type that command (8 images here):

$ caf -Ofast -march=native -mtune=native ppm_coarray_buddhabrot.f90 && cafrun -n 8 ./a.out

Intel ifx

$ ifx -Ofast -coarray ppm_coarray_buddhabrot.f90 && ./a.out

The number of images can be set with the option -coarray-num-images=8.

Flang

Flang 22.1 offers an experimental support for coarrays with the option -fcoarray.

TODO

• The loop computing z(k) could be stopped by exit when we escape the computing window containing the whole Mandelbrot set.
• We could use the symmetry of the Buddhabrot to improve computing.
• We could add colours instead of grey levels.

License

Distributed under the MIT license.

References

• Curcic, Milan. Modern Fortran - Building efficient parallel applications, Manning Publications, 1st edition, novembre 2020, ISBN 978-1-61729-528-7.
• Metcalf, Michael, John Ker Reid, et Malcolm Cohen. Modern Fortran Explained: Incorporating Fortran 2018. Numerical Mathematics and Scientific Computation. Oxford (England): Oxford University Press, 2018, ISBN 978-0-19-185002-8.
• Thomas Koenig, coarray-tutorial.
• Ondrej CERTIK's code (MIT license) for PPM format: https://github.com/certik/fortran-utils/blob/master/src/ppm.f90