Analysis of Laces and Meshes by means of Fractal Images and Dimensions.

Abstract

The shapes of meshes and laces were analyzed by means of a fractal geometry technique and simulated by fractal images such as a Sierpinski gasket, a Sierpinski carpet and their modified images. The image analyses of meshes, needlepoint laces, bobbin laces, and their models were discussed in detail. The followings were found: the renge of dimensions of the needlepoint laces and the bobbin laces were inbetween 1.5849 (the dimension of the Sierpinski gasket) and 2-dimensions. The correlation coefficients were lager than 0.999, accordingly the shape of the laces was a random fractal set, which is a kind of statistically self-similar obect. The geometric model of “Point couppe”, the origin of the needle laces which can be prepared by cutting a two dimensional cloth, corresponded to the Sierpinski carpet which has the dimension of about 1.9. In the course of the development of needlepoint laces from the “point couppe” to “reticellas”, which is made by using a grid of plaited threads instead of the residue of woven fabric to give larger and more openings and to give more delicate impression, and aurther to “punto-in-aria” which is called “the lace in the air” becase of its delicate appearance, it was found that the dimension changed from that of the cloth to that of the Sierpinski gasket, that is, from 2 to 1.5489.