Showing papers on "n-flake published in 2002"
Journal Article•
TL;DR: In this article, the concept of fractal geometry and general fractal examples in nature are introduced from a "strange" case in Euclidean space, and the principle and calculate formula of the fractal interpolation curve are given.
Abstract: From a "strange" case in Euclidean space, the concept of fractal geometry and general fractal exam-ples in nature are introduced. On the theory of iterated function system, the principle and calculate formula of fractal interpolation curve are given and the mathematical model of fractal interpolation surface on rectangle fi-eld is studied. Based on the measured data on a rock fracture surface, the rock fracture roughness surfaces are simulated.
6 citations
Journal Article•
TL;DR: In this paper, a new direct method for searching the global optimum of the restricted optimization problem is presented, which is called the fractal algorithm, and it can be easily extended to an optimization problem subjected to a parallelogram, an arbitrary polygon in plane or an arbitrarily polyhedral in space.
Abstract: The formation method of several basic geometric figures with fractal is given. By this method ,a new direct method for searching the global optimum of the restricted optimization problem is presented, which is called the Fractal algorithm. At the same time, a few examples show that the fractal method has the advantage over the common method, that it is not only independent of initial point but also adaptable for any nonlinear problem with an arbitrary polygon or polyhedral as the constraint condition. This algorithm makes full use of the characteristic that an arbitrary triangle, a tetrahedron or other basic geometric graphics can be filled by a fractal. It can be easily extended to an optimization problem subjected to a parallelogram, an arbitrary polygon in plane or an arbitrary polyhedral in space. Here the triangle and the tetrahedron are used as the constraint conditions.
1 citations
Journal Article•
TL;DR: In this article, a generalized Sierpinski carpet with contract radio was constructed, and their Hausdorff measure was proved to be ǫ 2 sǫ, where s is a real number.
Abstract: Based on the right polygon with edge 2m and diameter 2, a class of generalized Sierpinski carpets with contract radio 1∶k (k≥2m is a real number) is constructed, and their Hausdorff measure is proved to be 2 s, where s= log k 2m.
1 citations