How has the collision or clash of three worlds/civilizations impacted the culture of the USA today?
Your question wasn't too clear and have edited it, and I assume that you are asking about the 'clash of civilizations' (or worlds, in a sense), which formed the basis of Huntington's hypothesis?
Very simply, the idea of the clash/collision of civilizations was proposed as a theory or hypothesis by Samuel Huntington, an American Political Scientist , in an essay written and delivered as a lecture in 1992, later published as a book. According to Huntington, there are three (3) basic or 'major' civilizations in the world that have a 'clash' (collision) or will clash/collide, inevitably i.e. (a) the West/Western civilization (b) Islam/Muslim civilization and (c) Oriental/Far Eastern/ Chinese-dominated civilization-- they will clash or do already clash, because of various opposing economic, political, strategic global interests etc. Also, according to Huntington, there are some 'swing' civilizations, such as Japan, Russia, India , which can take any side, they don't have a fixed direction or interests.
USA is seen, of course as a 'leader' of Western civilization, of the West, and Huntington theory found lots of people to support it there--indeed, between 1990s and 2000s (present), many scholars and writers have criticized Huntington and the fallacies/mistakes in his ideas, and some have even said that in fact, Huntington's ideas have 'led to a clash' or even 'created' one, and not the other way round. The American-Lebanese scholar and writer Edward Said even said that this theory was in fact a 'Clash of ignorance', that if people around the world, various civilizations and cultures etc, tied to sit down and have a dialog and talk and get to know and respect each other, there would be no 'clash' or clashes, or collisions of any sort, really. However, somehow, this theory found a very strong support during the 1990s in the USA governments/establishment, and as a result, it was 'assumed beforehand' that there was a clash/collision or would be and America/Americans reacted accordingly, with hostility.
At the same time, in the so-called 'Islamic' or Muslim world, this theory and USA's reponse/adherence to it, in particular during the First Gulf War of 1991-92, met with great hostility and suspicion from the extremist elements; and by 2000-2001, these elements or fanatical groups misused the theory/idea for their own ends, i.e. to get back at the USA and West. This was the strengthening of Al-Qaeda and its various supporting groups all around , and led to 9/11 and then to the 2 wars-- in Afghanistan and Iraq-- which have bled the world dry and made the USA extremely unpopular in many parts and also deeply affected many nations, fighting or involved in this negative scenario.