Balankin Alexander S, Ochoa Didier Samayoa, Miguel Israel Andrés, Ortiz Julián Patiño, Cruz Miguel Angel Martínez
Grupo Mecánica Fractal, Instituto Politécnico Nacional, México D.F. 07738, México.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 1):061126. doi: 10.1103/PhysRevE.81.061126. Epub 2010 Jun 17.
We study the statistical topology of folding configurations of hand folded paper balls. Specifically, we are studying the distribution of two sides of the sheet along the ball surface and the distribution of sheet fragments when the ball is cut in half. We found that patterns obtained by mapping of ball surface into unfolded flat sheet exhibit the fractal properties characterized by two fractal dimensions which are independent on the sheet size and the ball diameter. The mosaic patterns obtained by sheet reconstruction from fragments of two parts (painted in two different colors) of the ball cut in half also possess a fractal scale invariance characterized by the box fractal dimension DBF=1.68 ± 0.04 , which is independent on the sheet size. Furthermore, we noted that DBF, at least numerically, coincide with the universal fractal dimension of the intersection of hand folded paper ball with a plane. Some other fractal properties of folding configurations are recognized.
我们研究手工折叠纸球折叠构型的统计拓扑结构。具体而言，我们正在研究纸张两面沿球表面的分布以及将球切成两半时纸张碎片的分布。我们发现，通过将球表面映射到展开的平面纸张上所获得的图案呈现出分形特性，其由两个与纸张尺寸和球直径无关的分形维数表征。通过将切成两半的球的两部分（用两种不同颜色绘制）的碎片进行纸张重建所获得的镶嵌图案也具有以盒分形维数(D_{BF}=1.68 ± 0.04)表征的分形尺度不变性，该维数与纸张尺寸无关。此外，我们注意到，至少在数值上，(D_{BF})与手工折叠纸球与平面相交的通用分形维数一致。折叠构型的一些其他分形特性也得到了确认。
