Group-separation effect in cell-size distribution of origami crease patterns

Some statistical properties of origami (the art of paper folding) are investigated. In a crease pattern of an origami work, a paper sheet is divided into many "cells" surrounded by creases. We compute the cell-size distributions of four origami works and find that they are described by the superposition of lognormal distributions with different averages and variances. This lognormal behavior can be explained by a successive-folding process that works as a multiplicative effect. To confirm this idea, we introduce a numerical model by only incorporating a successive-folding process, and discuss its analytical properties. Moreover, we show that a group-separation structure is also essential in origami, which is different from pure crumpling.