ComsystanJ: A collection of Fiji/ImageJ2 plugins for nonlinear and complexity analysis in 1D, 2D and 3D.

Complex systems such as the global climate, biological organisms, civilisation, technical or social networks exhibit diverse behaviours at various temporal and spatial scales, often characterized by nonlinearity, feedback loops, and emergence. These systems can be characterized by physical quantities such as entropy, information, chaoticity or fractality rather than classical quantities such as time, velocity, energy or temperature. The drawback of these complexity quantities is that their definitions are not always mathematically exact and computational algorithms provide estimates rather than exact values. Typically, evaluations can be cumbersome, necessitating specialized tools. We are therefore introducing ComsystanJ, a novel and user-friendly software suite, providing a comprehensive set of plugins for complex systems analysis, without the need for prior programming knowledge. It is platform independent, end-user friendly and extensible. ComsystanJ combines already known algorithms and newer methods for generalizable analysis of 1D signals, 2D images and 3D volume data including the generation of data sets such as signals and images for testing purposes. It is based on the framework of the open-source image processing software Fiji and ImageJ2. ComsystanJ plugins are macro recordable and are maintained as open-source software. ComsystanJ includes effective surrogate analysis in all dimensions to validate the features calculated by the different algorithms. Future enhancements of the project will include the implementation of parallel computing for image stacks and volumes and the integration of artificial intelligence methods to improve feature recognition and parameter calculation.

Kolmogorov compression complexity may differentiate different schools of Orthodox iconography.

The complexity in the styles of 1200 Byzantine icons painted between 13th and 16th from Greece, Russia and Romania was investigated through the Kolmogorov algorithmic information theory. The aim was to identify specific quantitative patterns which define the key characteristics of the three different painting schools. Our novel approach using the artificial surface images generated with Inverse FFT and the Midpoint Displacement (MD) algorithms, was validated by comparison of results with eight fractal and non-fractal indices. From the analyzes performed, normalized Kolmogorov compression complexity (KC) proved to be the best solution because it had the best complexity pattern differentiations, is not sensitive to the image size and the least affected by noise. We conclude that normalized KC methodology does offer capability to differentiate the icons within a School and amongst the three Schools.