And finally comes a question of relevance. During the golden age of Japanese anime in the ’80s and ’90s, foreign companies clamored for Japanese content because it represented the first they had ever seen of animation for an older audience. Although manga and anime still retain a certain cachet abroad, Americans and Europeans who grew up on Japanese creations are now happily creating their own films and series aimed at this demographic, domestically addressing the gap in demand that Japanese content once filled. American-produced shows such as “Avatar: The Last Airbender” and “The Boondocks” target older audiences with obvious anime flair, and Pixar’s John Lasseter has gushed that his smash hit “Toy Story” “owes a huge debt of gratitude to the films of Mr. Miyazaki.”