Seong-Gyun Im, Taewoo Kang, and S. Joon Kwon introduce a new method called Hilbert entropy to quantify the complexity of high-dimensional data by using space-filling curves like the Hilbert curve. This approach aims to reduce dimensions while preserving context, offering an alternative to traditional metrics such as Lyapunov exponents or fractal dimension that often fail to capture the intrinsic nature of complex physical systems. The authors validated this methodology through its ability to accurately identify critical phenomena and phase transitions in percolation models and spin models.
- Validated via high concordance with theoretical phase transition points.
- Demonstrates a potential linear relationship between scaling exponents and Euclidean dimensions for scale-invariant geometries.
- Applicable to 2D and 3D geometrical analysis of complex systems.
- Validated via high concordance with theoretical phase transition points.
- Demonstrates a potential linear relationship between scaling exponents and Euclidean dimensions for scale-invariant geometries.
- Applicable to 2D and 3D geometrical analysis of complex systems.
