This is not fan art—although the artist may well be a fan of the show—but the actual character design for Emperor Awesome and his Tyrannosaurus rex, created by Bryan Arnett. (You can also find him in my post on the “The Picnic” credits.)
About the final two images he writes:
Emperor Awesome pre-designs and final turn around. After a lot of revisions for this character Craig McCracken pulled it all together and did the final 3/4 front design. I did the other poses.
Curiously, it says “104” in several file names, which looks like an episode number. Was “The Picnic” originally 104 instead of 102a? Did they already adhere to the a/b suffix scheme during production? Maybe I should just ask.