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The Xenomorph in this movie is slightly different from others of his kind featured in the sequels in terms of behavior: unlike the other Aliens in the franchise, which kill only for food, host gathering, or self-defense, the Alien in this movie is implied multiple times in the movie, novelization, and several scripts to be very sadistic, and enjoys killing for fun. This is shown when the Alien kills Parker: he waits thirty seconds or so, while squeezing Parker so hard he bleeds, before finally killing him with a headshot.
The blue laser lights that were used in the alien ship's egg chamber were borrowed from The Who. The band was testing out the lasers for their stage show in the soundstage next door.
The chestbursting scene was NOT filmed in one take (despite the myth). The scene was filmed twice: on the first take, the chestburster did not make it through Kane's shirt, so the crew needed to reset and shoot it again. The failed attempt is visible in the finished film since Ridley thought it made it look like the creature was struggling to push its way out, and made the scene more violent. (See The Beast Within documentary where this is discussed).
Shredded condoms were used to create tendons of the beast's ferocious jaws.
According to Yaphet Kotto, Sir Ridley Scott told him to annoy Sigourney Weaver off-camera, so that there would be genuine tension between their characters. Kotto regretted this, because he really liked Weaver.
To get Jones the cat to react fearfully to the descending Alien, a German Shepherd was placed in front of him with a screen between the two, so the cat wouldn't see it at first. The screen was then suddenly removed to make Jones stop advancing and start hissing.