Perhaps it's their (the program's special effects team's) speculation that the view from within a warp field (or warp bubble) would appear refracted (rainbow-colored), as light passing through a medium such as a bubble, a prism, or an atmosphere does.
Sci–fi warp-travel (both within Star Trek and in other stories) has for decades been generally theorized to work by surrounding a ship in a field or bubble of warped space.
The Star Trek: The Next Generation Technical Manual (1991, p. 54) states that in-universe inventor Zephram Cochrane originally described his warp drive as a "continuum distortion propulsion."
The Alcubierre theory (1994) suggests a field/bubble that specifically contracts space ahead of the ship and extends space behind the ship, allowing the ship effectively to travel faster than light, without locally (within the field/bubble) breaking light-speed.
Memory Alpha describes Star Trek's warp drive thusly:
It worked by generating warp fields to form a subspace [warp] bubble that enveloped the starship1… The warp field was a subspace displacement that warps space around the vessel, allowing it to "ride" on a distortion and travel faster than the speed of light.2
The concept of warp-travel has been illustrated variously (both within Trek lore and by independent theorists) as below:
Interestingly, at least one person has suggested in Scientific American (2000) that a sort of combination of Einstein’s contraction/expansion and Doppler’s red–blue shift would more likely be visible:
As the velocity increases, stars ahead of the ship appear ever closer to the direction of motion and turn bluer in color. Behind the ship, stars shift closer to a position directly astern, redden and eventually disappear from view altogether.
Otherwise, it's difficult to draw yet any real-world examples. NASA and some private parties are exploring ideas, but they have yet to release macroscopic results.