Symmetry analysis on symmetry cognition on multilevel figures

The order of difficulty for identifying symmetries is analyzed by psychological experiments. Each stimulus consists of three squares: top, left and right. Each square is again divided into 4 × 4 squares (cells). Each cell has one iconic figure such as an arrow, circle, or rectangle. These three figures exhibit one of the symmetries: vertical reflection, horizontal reflection, diagonal reflection, 180 degree rotation. Symmetries are analyzed at two levels: global coordination (the global cell-to-cell correspondence pattern) and local operation (how the iconic figure is rotated within each cell). The order of difficulty is determined not only by the independent global coordination type and by the local operation type, but by the pairwise comparison of global coordination types, i.e., how difficult it is to discriminate two global coordination types.