The rapid advancement of Artificial Intelligence (AI) systems has raised critical questions about their social, ethical, and practical implications. Many of these technologies are made by the few to represent the many, resulting in a considerable amount of harmful biases. While extensive research exists on AI bias and ethics, there lacks a comprehensive framework for understanding how culture, the foundation of bias, manifests in AI systems in ways that could impede the development of the emerging Artificial General Intelligence (AGI). This paper proposes aTi (pron. Ah Tee), a framework for holistically studying and quantifying cultural emergence in AI systems. We base aTi on four key components: values, behavioral patterns, decision algorithms, and experiences, which serve as activation points where culture can emerge. Our framework categorizes artificial intelligent systems into first-order and second-order artificial culture categories, offering a nuanced approach to understanding the complexity of cultural emergence in AI systems for AGI. Through case studies, we demonstrate the practical application of our framework and explore its implications for future AI development. This work contributes to the growing discourse on responsible AI development by providing a systematic approach to understanding and addressing cultural considerations in AI systems.