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Sir Ian Holm and Sir Ridley Scott recalled that one day, as Ridley rolled into the studio in his Rolls-Royce, Sigourney Weaver quipped, "Nice car. Did your dad buy it for you?" The comment really irked Scott, but Holm seemed to observe that she was yanking Scott's chain, having recognized him as being self-made and proud of it.
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.