The parks department has helpfully erected an informational plaque next to the bench, identifying the carver as William Galloway, who created the piece in 1989, when it won the Hoosierfest Limestone Bench Carving Contest. I was happy to see that the bench's weirdness is acknowledged, though it's not fully explained:
Originally, the sculpture was meant to be carved in the shape of a Stegosaurus, but since Stegosaurus don't have sail-backs, the artist chose Dimetrodon so people would have a place to lean their backs. Not wanting to give up the large loop on the bench, a Stegosaurus tail was added, making this bench a hybrid dinosaur of sorts.I'd guess that the design changed before carving ever began, with the spiky tail the only part of the original sketches to be retained. Call it artistic license. The plaque does explain that Dimetrodon was not a dinosaur, which is great, but it's a bit muddled on evolutionary history, noting that "dinosaurs eventually evolved into modern day reptiles and birds" and that Dimetrodon is "actually an early ancestor of modern day mammals." A few points for effort, I suppose.
Update 1/6/13: Meant to include that this is, as indiated in comment by Mark Robinson, in Bloomington's Bryan Park. It's a real nice park.