The Fractal Dimension and Universal Logical Operation of Cantor-Set Based on Grid Image
基于格图像的康托集分维与泛逻辑运算

The study of cantor-set is classical but heated subject in fractal field. This paper tries to study the fractal characteristic of cantor-set by a new model called "grid image", gives the method of construction of grid image and calculation of fractal dimension. The results show that the self-similar dimension is the specialty of grid image dimension, and the grid image dimension is the extended case of self-similar dimension. The paper imports the conception of universal logic firstly, gives the operation models of "NOT", "AND", and "OR" based on grid image. They take into account not only the values of algebraic measure but also the relationship of geometric location. This work provides a new thought-way for studying fractal image, and enlarges the applied fields of universal logic.