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The red herring with the cat and Brett's death were originally storyboarded to take place at the same moment. The crew finds the cat through the tracker, and it bursts out of the locker. With the signal still beeping, the crew crouches down waiting for the chestburster to follow. Looking down at the floor, they see the fully grown Alien's feet, and slowly look up at it towering over them as the creature seizes Brett, snaps his spine and disappears into the darkness with his body, leaving Ripley and Parker watching. It's also interesting to note that they initially had planned for the Alien to punch Brett's heart out.
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 was unable to cut through Kane's shirt, so the crew needed to reset and shoot it again. The failed attempt is visible in the finished film, since director Ridley Scott 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). According to designer Ron Cobb, the two takes of the scene were shot from multiple angles, and about 40 minutes of footage was available for screening.
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.