Interpretable liquid crystal phase classification via two-by-two ordinal patterns

Interactive visualization of liquid crystal texture ordinal-pattern space. This visualization presents a UMAP projection where each point represents a texture from our dataset, positioned according to its ordinal-pattern distribution across the 75 possible two-by-two ordinal patterns. Textures are color-coded and marked by distinct symbols corresponding to their mesophase classification. By hovering your mouse over any point, you can view the ordinal distribution (displayed as circular bars on a logarithmic scale) along with the corresponding texture image for that specific sample. The visualization also features interactive legend controls — clicking on any mesophase symbol allows you to selectively show or hide textures belonging to that category, enabling focused exploration of specific mesophase patterns or comparative analysis between different phases. This interactive approach allows for dynamic exploration of how different liquid crystal mesophases cluster in the ordinal-pattern space and reveals the characteristic ordinal patterns associated with each texture type.

For more details, please refer to our paper.

• Leonardo G. J. M. Voltarelli, Natalia Osiecka-Drewniak, Marcin Piwowarczyk, Ewa Juszyńska-Gałązka, Rafael S. Zola, Matjaž Perc, and Haroldo V. Ribeiro, Interpretable liquid crystal phase classification via two-by-two ordinal patterns, Journal, number, pape (year)