lzcomplexity

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

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.