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Fractals reveal intricate, self-similar patterns repeating across infinite scales, while chaos captures the profound sensitivity to initial conditions that turns order into unpredictability. Hidden dimensions—often invisible in traditional Euclidean space—unlock deeper insight into systems where structure and randomness coexist. This interplay manifests in number theory, dynamical systems, and even playful simulations like Chicken vs Zombies, where branching choices generate complex, fractal-like outcomes. Understanding these dimensions not only enriches mathematics but also informs how information flows and systems evolve in nature and digital worlds. What unites these diverse realms? The subtle geometry underlying randomness and feedback.

Riemann’s Fractal Landscape: Primes and the Edge of Randomness

At the heart of number theory lies the Riemann zeta function,

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