J.G. Freire, Brison, O.J. and Gallas, J.A. (2009) Exact Quantification of the Complexity of Spacewise Pattern Growth in Cellular Automata. Journal of Physics A: Mathematical and Theoretical, 42, Article ID: 395003.
https://doi.org/10.1088/1751-8113/42/39/395003

has been cited by the following article:

• TITLE: Novel Lossless Compression Method Based on the Fourier Transform to Approximate the Kolmogorov Complexity of Elementary Cellular Automata

  AUTHORS: Mohammed Terry-Jack

  KEYWORDS: Fast Fourier Transform, Lossless Compression, Elementary Cellular Automata, Algorithmic Information Theory, Kolmogorov Complexity

  JOURNAL NAME: Journal of Software Engineering and Applications, Vol.15 No.10, October 26, 2022

  ABSTRACT: We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics1.