Pixiv Red, or Fandom Red, is a depiction of Red that became very popular on Japanese art sharing websites like Pixiv during the late 2000s to early 2010s. He is a version of the Red that appears on Mt. Silver in Pokemon HGSS.
Departing from the game's design, this fandom version had short, loose black hair and red eyes (sometimes black, brown, or grey). He was slim, if not toned, with a stoic face and a cool persona. His feelings were usually kept very subtle.
When depicted with a Pokemon, he usually favored Charizard as his main, or was drawn with Pikachu as his companion.
Take note: not every Red depicted as stoic, with black hair, and/or with red eyes is a Pixiv Red. The hair on a typical depiction of Pixiv Red is more relaxed and glossy and does not fan out to the sides, a la post #2278447. His eyes aren't very wide either, compared to his official counterpart.
This tag implicates red_(pokemon) (learn more).