Measuring the strangeness of strange attractors¶
Grassberger, P., & Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, 2789(83), 1-2.
Cited by¶
4 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Chaos
- 6. Mixing and structure: despite apparent disorder, the attractor has a characteristic structure (often fractal, with non-integer Hausdorff dimension as Grassberger and Procaccia (1983) operationalized through the correlation dimension)
This sourceIntroduces the correlation dimension as a computationally tractable measure of fractal attractor dimension and a diagnostic distinguishing low-dimensional chaos from high-dimensional noise.
- 6. Mixing and structure: despite apparent disorder, the attractor has a characteristic structure (often fractal, with non-integer Hausdorff dimension as Grassberger and Procaccia (1983) operationalized through the correlation dimension)
Domain-specific¶
- Correlation Dimension
- For finite data, the Grassberger–Procaccia estimator counts close pairs over a range of radii and estimates the slope of `log C_N(r)` against `log r` in a defensible scaling region.
This sourceDevelops the estimator, scaling interpretation, and comparisons with other dimensions.
- For finite data, the Grassberger–Procaccia estimator counts close pairs over a range of radii and estimates the slope of `log C_N(r)` against `log r` in a defensible scaling region.
- Correlation integral
- Its small-radius scaling estimates correlation dimension, but temporal dependence, finite samples, noise, embedding choices and edge effects require exclusion windows and a defensible scaling region.
- The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Verification¶
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://verga.cpt.univ-mrs.fr/pdfs/Grassberger-1983fk.pdf ×1
- https://www.sciencedirect.com/science/article/pii/0167278983902981 ×1
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