Yes, now animated GIFs can be created using only Fortran code. I present FGIF, now on GitHub. It is a modified and updated version of the public domain code found on the Fortran Wiki. It was used to create the image shown here (which is an example of a circle illusion).
For more information on the GIF format, see:
It was interesting to discover that animated GIFs are actually a Netscape extension to the GIF file format. If you open any animated GIF in a hex editor, you will find the string “NETSCAPE2.0”.