The Beach

Richard, a young American seeking adventure in Bangkok, meets the eccentric Daffy, who tells him of a pristine, uninhabited island in the Gulf of Thailand with a beautiful hidden beach and lagoon. Daffy explains that he and other travelers settled there in secret several years earlier, but difficulties arose and he chose to leave. Daffy commits suicide, leaving Richard a map to the island. Richard convinces a young French couple, FranÃ§oise and Ãtienne, to accompany him to the island, and the three travel to Ko Samui. Richard meets two Americans who have heard rumors of the island, including that huge amounts of cannabis supposedly grow there. Before departing, Richard leaves them a copy of the map.
En route to the island, Richard becomes infatuated with FranÃ§oise. After swimming to the island from a neighboring one, they find a large cannabis plantation guarded by armed Thai farmers. Avoiding detection, they make their way across the island and are welcomed into the secret beach settlement. The community's leader, Sal, explains that the farmers allow them to stay so long as they keep to themselves and do not allow any more travelers to come to the island. Richard lies that they have not shown the map to anyone else, which satisfies Sal. The trio become integrated into the largely self-sufficient and leisurely community. The relationship between Richard and FranÃ§oise becomes romantic, and Ãtienne says he will not stand in their way if FranÃ§oise is happier with Richard. Tensions rise between Richard and Sal's boyfriend Bugs; when Richard gains celebrity by killing a shark, Bugs mocks him over the shark's small size.
When Sal selects Richard to accompany her on a supply run to Ko Pha Ngan, Bugs warns him to keep his hands off her. While there they encounter the Americans Richard met in Ko Samui, who are preparing to search for the island and mention Richard's map. Richard lies to Sal that he did not give them a copy, and she blackmails him into having sex with her. On their return to the island, Richard lies to FranÃ§oise about having slept with Sal. Things return to normal until a shark attack kills one of the community's fishermen and leaves another, Christo, severely injured. Sal refuses to compromise the community's secrecy by bringing medical help, and Christo refuses to travel to the mainland. His worsening condition affects the group's morale, so they isolate him in a tent despite Ãtienne's objections.
When the Americans from Ko Pha Ngan turn up on the neighboring island, Sal sees that they have a copy of the map and orders Richard to observe them until they cross over, then intercept them and destroy it. She tells everyone that she and Richard had sex, which leaves FranÃ§oise angry and heartbroken. Isolated from the group, Richard begins to lose his sanity, stalking the cannabis farmers and imagining that he is conversing with the deceased Daffy. The Americans reach the island but are discovered and killed by the farmers. Shocked at witnessing their deaths, Richard tries to gather FranÃ§oise and Ãtienne to leave the island. Ãtienne refuses to leave Christo, whose leg has become gangrenous, so Richard euthanizes Christo by suffocation.
Richard is captured by the farmers and brought before the community. The lead farmer gives Sal a gun loaded with a single bullet and orders her to make a choice: kill Richard and the group will be allowed to stay, or else they must all leave immediately. Sal pulls the trigger, but the chamber is empty. Shocked by her willingness to commit murder, the community abandons Sal, leaving the island and going their separate ways. Later, Richard receives an email from FranÃ§oise with a group photograph of the beach community in happier times.

Question: What are the Americans searching for?
Answer: The Island mentioned in Richards map.