In the last five years there has been a marked increase in the migration flows in the countries of the western world. This increase has led, in many cases, in the empowerment of xenophobic and nativist political forces, and an active conversation regarding the compatibility, integration, and conflict of different civilizations and cultures. In this study we investigate the effect of various cognitive and cultural factors in the integration of new populations in a society during a number of generations. We use agent-based modeling and an extended version of the Schelling segregation model. The model supports heterogeneity of fundamental parameters and lookahead evaluation of new positions as in , advanced motion and type-imitation or cultural assimilation modes, as well as differential perception of different populations via a weighting rule. We show how different parameter configurations can model various realistic ethnic/cultural responses to newcomers, such as a Danish, an American and a Hungarian model. We model societies that consist of natives, first-generation and second-generation immigrants and we demonstrate that in certain environments, the least overall tolerant subpopulation remains in constant move in an otherwise segregated social environment. Moreover, we study multi-ethnic but stable societies after a new population is injected (immigrates) and we show how this can lead to markedly higher ethnic segregation for the original communities as a defense against the massive immigration and/or to marginalization of newcomers etc. (See figure below, before and after injection) We also investigate the classical finding of sociology, according to which the attitudes of second generation immigrants are correlated with the degree of integration of their parents; the general rule is that the immigrants whose parents are not well integrated are more conservative and less welcoming of new immigrant arrivals. Finally, we discuss how the above can apply to vectors of many populations that co-exist and/or meet in the same interaction environment.