Zipf's law, 1/f noise, and fractal hierarchy

Understand

Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within the specific scientific domains.

• All these observations are associated with scaling laws and have caused a broad research interest in the scientific circle.
• However, the inherent relationships between these scaling phenomena are still pending questions remaining to be researched.
• In this paper, theoretical derivation and mathematical experiments are employed to reveal the analogy between fractal patterns, 1/f noise, and the Zipf distribution.