In this study, I use a computer simulation model to investigate one possible process of cultural polarization in modern society. Numerous studies have used computer simulation models based on the principle of homophily to explain the process of cultural or political polarization and convergence. Most of these assume (1) network structure is fixed and (2) an actor’s ecology, in terms of possible interactions with others, is randomly decided. In contrast to (1), I assume network structure to be dynamic such that it consists in part of a non-trivial amount of non-structuralized, i.e., temporary, weak ties. I take this to be a reasonable assumption because the development of institutional certainty has improved levels of generalized trust, and technology, for example, through the development of online communities, has made it possible for actors to interact with unanticipated actors without the complicated process of building mutual trust. In contrast to (2), I assume that actors are initially embedded in homophily groups. This is because induced homophily (at the macro level) and repeated choice homophily processes (at the micro level) mean that an actor’s close ties are likely to consist of similar actors. I investigate the effects of these two assumptions by modifying the simulation model developed by Flache and Macy (2011). The first simulation experiment shows that while structuralized weak ties, commonly used in previous studies, lead to cultural polarization, non-structuralized weak ties and homophily subnetworks tend to produce cultural convergence. The second experiment suggests why this is so. When weak ties are structuralized, the influence from dissimilar actors, which produces polarization, is always stronger than the influence from similar actors. When weak ties are non-structuralized, the early influence of similar actors tends to be stronger, which, coupled with the push toward convergence from the homophily subnetwork, tends to produce convergence. In the third experiment, I suggest two new models of cultural polarization, based on the findings from the second experiment: 1) a mixed model with non-structuralized and structuralized weak ties, and 2) a model with non-structuralized weak ties under a firmly polarized cultural value. The two new models exhibit polarization results and processes not seen in previous simulation studies. They constitute potential new theoretical models for cultural polarization in modern society.