Impossible figures’ morphological recognition and analysis of inconsistent rectangles

A basic study for digital works relating to impossible figures

Abstract

Impossible figures are known to be motifs of the Dutch artist M. C. Escher's lithographs. However, impossible figures cannot be strictly defined geometrically because they are mental images of solid objects. In other words, viewers perceive two-dimensional (2D) drawings as three-dimensional (3D) structures, although these structures cannot be realized in 3D space. Regardless of the mental images, viewers’ morphological different recognition of impossible figures have not been sufficiently researched; thus, we performed two experiments to address this gap. In the first experiment, the participants observed each sample figure individually in random order and then stated whether, according to them, it was an impossible or possible figure. Approximately half the participants labeled some sample figures as possible figures in spite of them being impossible geometrically. The results indicated that perceptions of impossible figures differ according to the individual and the figures themselves. We also obtained widely differing results between four inconsistent rectangles that had the external contours of possible rectangles. To address this variability, we focused on the inconsistent rectangles in the second experiment. The four rectangles were sub-classified into 28 categories, and the participants were asked whether each of the 28 figures was impossible or possible, similar to the procedure followed in the first experiment. The sub-classified rectangles were broken down into polygons to analyze the results. Finally, we extracted an element that led to participants' perception of possible figures and two elements that led to their perception of impossible figures.