lzcomplexity
Randomness, structure and similarity in symbolic sequences.
Explore how a sequence balances unpredictability and organization, or compare
the patterns shared by different sequences. lzcomplexity brings Lempel–Ziv
analysis to Python and standalone command-line tools, powered by a Rust core.
| Measure | What you can explore |
|---|---|
| Entropy density h | Unpredictability, the production of new information and freedom of choice within a sequence. |
| Effective measure complexity E | Organization and correlations across different ranges of a sequence. |
| Information distance d | Similarity between sequences through the patterns they share. |
Use h and E together to distinguish changes in randomness from changes in organization. Use d to compare recordings, texts or symbolic trajectories.
Start in Python
pip install lzcomplexity
import lzcomplexity as lz
sequence = "00010111" * 256
other = "01010101" * 256
h = lz.h(sequence, log_base=2) # Randomness
E, increments = lz.emc(sequence, max_block_size=16) # Structure across ranges
d = lz.nid(sequence, other) # Distance between sequences
E defaults to Chao–Shen block entropy estimation. Use
lz.emc(sequence, method="shuffle") or lz.lz76(sequence, method="shuffle")
for the earlier random-shuffle estimator. The standalone accepts
--emc-method shuffle; -e 8:f still chooses the range and profile output.
Pass text or bytes directly. For categorical data, assign one byte to each symbol; for continuous signals, first choose a symbolic representation. The Python reference documents each function. The separate usage cheatsheet collects the common calls.
From the terminal
Download the standalone tools from GitHub Releases.
lzcomplexity recording.txt -F text -l 2 # Analyze a sequence; write a JSON report
lzdistance sequences.txt -I TXT # Compare one sequence per line
The command-line guide covers file formats, batch analysis and distance matrices, with a separate usage cheatsheet.
Research applications
These studies show the kinds of scientific questions that entropy, structure and distance can help investigate:
| Application | Explore |
|---|---|
| Nonlinear dynamics | Transitions between collective patterns and chaos in coupled Adler-type oscillators (Physical Review E, 2023). |
| Brain activity | Patterns and connectivity across brain regions during cognitive tasks in task-based fMRI (arXiv preprint, 2025). |
| Written language | The balance between innovation and context at different levels of text organization (PLOS ONE, 2019). |
See the worked examples and research references to develop an analysis for your own data.
Authors & citation
- Efrén Aragón Pérez — creator and principal author.
- Daniel Estévez Moya — Rust implementation.
- Ernesto Estévez Rams — scientific foundations.
Aragón-Pérez, E., & Estevez-Rams, E. (2025). Lzcomplexity: Entropy Measurement Library. Revista Cubana de Física, 42(2), 80–86. Article · Software DOI · BibTeX
Released under the MIT license.
Release files for lzcomplexity 3.0.0
For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
Source distribution (sdist)
| File | Size | Uploaded | Provenance | Actions |
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| lzcomplexity-3.0.0.tar.gz | 39.2 kB | With provenance | Details for lzcomplexity-3.0.0.tar.gz |
Built distributions (wheels)
| File | Actions Reset | |||
|---|---|---|---|---|
| lzcomplexity-3.0.0-cp39-abi3-win_amd64.whl | CPython 3.9 | abi3 | Windows x86-64 | Details for lzcomplexity-3.0.0-cp39-abi3-win_amd64.whl |
| lzcomplexity-3.0.0-cp39-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.whl | CPython 3.9 | abi3 | Linux glibc 2.17+ x86-64 | Details for lzcomplexity-3.0.0-cp39-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.whl |
| lzcomplexity-3.0.0-cp39-abi3-manylinux2014_aarch64.manylinux_2_17_aarch64.whl | CPython 3.9 | abi3 | Linux glibc 2.17+ ARM64 | Details for lzcomplexity-3.0.0-cp39-abi3-manylinux2014_aarch64.manylinux_2_17_aarch64.whl |
| lzcomplexity-3.0.0-cp39-abi3-macosx_11_0_arm64.whl | CPython 3.9 | abi3 | macOS 11.0+ ARM64 | Details for lzcomplexity-3.0.0-cp39-abi3-macosx_11_0_arm64.whl |
| lzcomplexity-3.0.0-cp39-abi3-macosx_10_12_x86_64.whl | CPython 3.9 | abi3 | macOS 10.12+ x86-64 | Details for lzcomplexity-3.0.0-cp39-abi3-macosx_10_12_x86_64.whl |
Total release size: 1.4 MB
Release files / lzcomplexity-3.0.0.tar.gz
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