A Property of Point Symmetry under Symmetric Folding Transformation

This paper examines the characteristics of point symmetry under a symmetric folding transformation. It demonstrates that, under such a transformation, a dataset exhibiting point symmetry within a rectangular region will be folded into a symmetric configuration with respect to one of the rectangle's mirror axes. This property can transform specific, regularly distributed datasets into nearly random distributions, beneficial for designing randomized algorithms, which have been widely employed in computer science and technologies.