The creative potential of generative AI models in producing original cultural artifacts remains a subject of debate. This paper investigates the hypothesis that visual art contains a vast unexplored space of conceptual combinations, constrained not by inherent incompatibility, but by cognitive limitations imposed by artists' cultural, temporal, geographical and social contexts. We specifically address the availability bias, where the ease of recalling familiar concepts limits the exploration of novel ideas.We introduce the Alien Recombination method, which utilizes two fine-tuned large language models (LLMs) to generate and rank novel combinations of artistic concepts by modeling and counteracting human cognitive biases. This system not only produces combinations that have never been attempted before within our dataset but also identifies and generates combinations that are cognitively unavailable to all artists in the domain. Additionally, we transform these combinations into images to assess more subjective perceptions of novelty.Our results suggest that cognitive unavailability is a promising metric for optimizing artistic novelty, outperforming merely temperature scaling without additional evaluation criteria.This approach employs generative models to connect previously unconnected ideas, offering a new perspective on AI creativity as a combinatorial process.