Quantum mechanics, while remarkably successful, presents a profound challenge: the inherent unpredictability of its outcomes. This paper explores the concept of geometric chaos, a novel approach to quantifying this unpredictability by directly analyzing the geometric structure of quantum states. We propose a new mathematical representation of quantum states that incorporates geometric properties to reveal patterns of randomness, ultimately demonstrating that the state space of a quantum system is not deterministic but rather exhibits complex, non-intuitive patterns. We present a preliminary framework for this analysis and discuss its potential implications for our understanding of quantum mechanics.