We present an approach for generating a sort of fractal graphs by a simpleprobabilistic logic neuron network and show that the graphs can be representedby a set of compressed codings. An algorithm for quickly finding ...We present an approach for generating a sort of fractal graphs by a simpleprobabilistic logic neuron network and show that the graphs can be representedby a set of compressed codings. An algorithm for quickly finding the codings,i.e., recognizing the corresponding graphs, is given. The codings are shown tobe optimal. The results above possibly give us the clue for studying imagecompression and pattern recognition.展开更多
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the...Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
文摘We present an approach for generating a sort of fractal graphs by a simpleprobabilistic logic neuron network and show that the graphs can be representedby a set of compressed codings. An algorithm for quickly finding the codings,i.e., recognizing the corresponding graphs, is given. The codings are shown tobe optimal. The results above possibly give us the clue for studying imagecompression and pattern recognition.
文摘Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
