Learned from Greek and Egyptian mythologies, underground comics, the art of Francis Bacon, and the dark visions of Dan O'Bannon and H.R. Giger. A contemplation on the symbiotic collaborative process of movie-making, the power of myth, and our collective unconscious.
What's about Mayan culture? They are excellent in Calendar and Time. There is Aliens vs Predators movie that has a secret of the Mayan complex structure. Great creation!
Thanks to @Dr. Dank for making me looking for more specific information:
Started with Necronomicon by HP Lovecraft that influenced HR Giger. Giger's Necronomicon was published in 1977. Giger’s Necronom IV was completed in 1976 which O’Bannon saw and approved his design for the movie. Special Effects designer Carlo Rambaldi designed and constructed Xenomorph.
Where did HR Giger get idea of Xenomorph???