Rocky the "rock" is light brown in color and is the same size as a snail (Gary, Snellie, and Larry Luciano) Also, it looks like a scaled down version of Patrick's rock.
Patrick enters Rocky in a snail race competing against Gary and Squidward's snail, Snellie. Somehow, it actually wins the snail race. It somewhat resembles a snail, but with a rock for a shell in the episode "The Great Snail Race."
In "Buried in Time," Patrick wants to donate Rocky to the Time Capsule. In this episode, however, Rocky is lumpy and gray, maybe meaning that he somehow got older.
In "The Great Snail Race," Rocky does not move, but at the end he is last seen on the finish line.
Perhaps the Mayor put Rocky at the finish line.
Rocky could have won by Patrick helping him along the track without stepping on the track himself, but that begs the question of why Patrick wasn't disqualified for setting foot on the track.
According to Patrick, Rocky has nerves of steel. Patrick even keeps saying "I know, I know, he's got nerves of steel."
In "Buried in Time," Rocky looks lumpier and he is gray.
Patrick could actually own three pet rocks. Two are named Rocky and one is named Pete.
Rocky is also in the beginning of "Patrick's Staycation." When SpongeBob says "Ooh, a shadow puppet show," Patrick says, "SpongeBob, please." while holding a rock that looks like his own.
Rocky is a smaller version of Patrick's rock, only without an antenna.