The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Easily calculable measure for the complexity of spatiotemporal patterns
Abstract
We demonstrate by means of several examples that an easily calculable measure of algorithmic complexity c which has been introduced by Lempel and Ziv [IEEE Trans. Inf. Theory IT-22, 25 (1976)] is extremely useful for characterizing spatiotemporal patterns in high-dimensionality nonlinear systems. It is shown that, for time series, c can be a finer measure for order than the Liapunov exponent. We find that, for simple cellular automata, pattern formation can be clearly separated from a mere reduction of the source entropy and different types of automata can be distinguished. For a chain of coupled logistic maps, c signals pattern formation which cannot be seen in the spatial correlation function alone.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A formal theory of inductive inference. Part II
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90131-7 · Cited by 1,758
On the Length of Programs for Computing Finite Binary Sequences
Chaitin, G. J. (1966) · Journal of the ACM · doi:10.1145/321356.321363 · Cited by 913
Cited by
A theoretically based index of consciousness independent of sensory processing and behavior
Casali, A. G., Gosseries, O., Rosanova, M., Boly, M., Sarasso, S., Casali, K. R., Casarotto, S., Bruno, M.-A., Laureys, S., Tononi, G., et al. (2013) · Science Translational Medicine · doi:10.1126/scitranslmed.3006294 · Cited by 1,246
Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines
Yan, R., Liu, Y., & Gao, R. X. (2012) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2011.11.022 · Cited by 377
Szechtman, H., Sulis, W., & Eilam, D. (1998) · Behavioral Neuroscience · doi:10.1037/0735-7044.112.6.1475 · Cited by 315
Abásolo, D., Hornero, R., Gómez, C., García, M., & López, M. (2006) · Medical Engineering & Physics · doi:10.1016/j.medengphy.2005.07.004 · Cited by 313
Spatiotemporal chaos in one- and two-dimensional coupled map lattices
Kaneko, K. (1989) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(89)90117-6 · Cited by 305
Metadata
- Authors
- Kaspar, F., & Schuster, H. G.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1987-07-01
- Volume
- 36
- Issue
- 2
- Pages
- 842-848
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2000832731
- Cited by
- 505
- References
- 2
- FWCI
- 4.24
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Easily calculable measure for the complexity of spatiotemporal patterns. https://app.cochat.ai/papers/10.1103/physreva.36.842
- The paper
- Kaspar, F., & Schuster, H. G. (1987). Easily calculable measure for the complexity of spatiotemporal patterns. Physical Review A. https://doi.org/10.1103/physreva.36.842
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
