Shannon (Information) Measures of Symmetry for 1D and 2D Shapes and Patterns

In this paper, informational (Shannon) measures of symmetry are introduced and analyzed for patterns built 1D 2D shapes. The measure Hsym(G) characterizes the averaged uncertainty in presence elements from group G a given pattern, whereas Shannon-like Ωsym(G) quantifies appearance shapes possessing total n belonging to pattern. Hsym(G1)=Ωsym(G1)=0 irregular, non-symmetric shapes, where G1 is identity element group. Both intensive parameters pattern do not depend on number their size, entire area They also insensitive long-range order (translational symmetry) inherent Additionally, fractal addressed, mixed including curves considered, time evolution Shannon examined, close-packed dispersed analyzed, an application suggested analysis chemical reaction demonstrated.