Virtual Reality allows for the ultimate immersion in environments not naturally encountered. Still, hyperbolic environments are extremely difficult to get used to. This paper explores whether immersion in virtual hyperbolic environments can be enhanced by introducing a procedurally generated world. We propose a Wave Function Collapse (WFC) algorithm that can divide the hyperbolic plane into distinct areas and populate the space with dynamically generated objects. This can assist players in recognising areas visited prior, which can create an intuitive feel for how hyperbolic space operates. Although 5-order square tiling is used in this paper, the proposed algorithm can be extended to other tiling approaches. Evidence suggests players in a populated hyperbolic environment need on average fewer steps to reach their objective compared to a control group with an empty environment, although the time taken for both groups is roughly the same. From this and a qualitative analysis we infer that players feel more immersed in the environment when it is procedurally generated instead of mostly empty.