Yet every brush stroke was painted only once.

A painted background is one flat picture: a camera can slide across it, but fly into it and it only swells. Tarzan needed "10 minutes of painterly looking, densely lush jungle" that a camera could move through, "with a relatively small crew". Repainting every frame by hand is, in Disney's own patent, "a prohibitive expense", and a jungle built as computer graphics has hard, clean edges, not paint. Eric Daniels, who led the film's computer graphics, built Deep Canvas with Tasso Lappas and George Katanics: the artist paints one view, every stroke is placed on the surface it lands on in 3D, and the computer repaints the picture from every new camera. In his words: "We are actually re-painting the background for each frame, by just moving the brush strokes a little bit." The gaps the camera uncovers get new strokes. It won a Technical Achievement Award in 2003.

Every frame of this film was painted the same way, by our own code: our own jungle, our own 3D strokes, no frames from any film.

Which shot in an animated film made you want to step inside the background?

Sources: Eric Daniels, "Deep Canvas in Disney's Tarzan", SIGGRAPH 1999; US Patent 6,268,865, Daniels, Lappas, Katanics, "Method and apparatus for three-dimensional painting" (Disney, 1998); Academy Scientific and Technical Awards, 2003; Mike Lyons, "Deep Canvas", Cinefantastique, August 1999.
Sounds: our own, made in code (earshot, CC0).