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5th International Conference on Neural Computing for Advanced Applications (NCAA)

作者： Wang, Ming Zuo, Lingchen Gong, Yanling Song, Yuanyuan Zhao, Qianchuan Zheng, Xuehan Gao, He Shandong Jianzhu Univ Sch Informat & Elect Engn Jinan 250101 Peoples R China Shandong Zhengchen Technol Co Ltd Jinan 250101 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

ISBN: (纸本)9789819770007;9789819770014

This paper proposes an innovative approach for generating the topology of artificial neural networks. The proposed method utilizes an iterative function system (IFS) to produce coordinate coordinates for neurons, enabling the construction of the input layer, hidden layer, and output layer topologies. The suggested method differs from conventional fully connected or convolutional neural networks in that it does not depend on a predetermined architecture. Instead, it is built dynamically through iterative calculations. The experiment involved the construction of a feedforward neural network with a single hidden layer. The connection topology of the neural network was generated using the IFS approach. Empirical findings demonstrate that the produced neural network has a high level of responsiveness to sine wave input signals. Additionally, an assessment was conducted on the network's performance, encompassing the computation of the correlation coefficient between the output signal and the input signal, the variance and standard deviation of the output signal, as well as the reaction time. This study presents a novel approach for the automated development of neural network architecture, demonstrating great potential.

关键词： Neural networks Automatic generating iterative function system

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A new fractal algorithm to model discrete sequences

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Chinese Physics B 2010年第9期19卷 274-278页

作者：翟明岳 Heidi Kuzuma James W. Rector School of EE Engineering North China Electric Power University Department of Civil Engineering University of California Lawrence Berkeley Laboratory

Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.

关键词： fractal interpolation the vertical scaling factors iterative function system seismic data

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Computing with continuous objects: a uniform co-inductive approach

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MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE 2021年第2期31卷 144-192页

作者： Spreen, Dieter Univ Siegen Dept Math D-57068 Siegen Germany

A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets and uniformly continuous maps is presented. In the work of Berger, it was shown how to extract certified algorithms working with the signed digit representation from constructive proofs. Berger and the present author generalised this approach to complete metric spaces and showed how to deal with compact sets. Here, we unify this work and lay the foundations for doing a similar thing for the much more comprehensive class of compact Hausdorff spaces occurring in applications. The approach is of the same computational power as Weihrauch's Type-Two Theory of Effectivity.

关键词： Computing iterative function system topology compact set inductive co-inductive definition program extraction

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Geometry control of the junction between two fractal curves

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COMPUTER-AIDED DESIGN 2013年第2期45卷 424-431页

作者： Podkorytov, Sergey Gentil, Christian Sokolov, Dmitry Lanquetin, Sandrine Univ Burgundy Dijon France Univ Lorraine Metz France

The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated function system model. Then we deduct the conditions that guarantees continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterise the differential behaviour at the connection points between the curves and the intermediate one. This behaviour depends on the nature of the initial curves and coefficients of the subdivision matrices. We also suggest a method to control the differential behaviour by adding intermediate control points. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： iterative function system Attractor Curve Differentiability

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Radar target recognition with fractal technology

Radar target recognition with fractal technology

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Conference on Signal and Data Processing of Small Targets 1996

作者： Deny, LP BEIJING INST TECHNOL DEPT ELECT ENGNBEIJING 100081PEOPLES R CHINA

ISBN: (纸本)0819421405

This paper presents an approach to radar target classification using fractal geometry techniques. The classification techniques used here exploit the geometric nature of the target and its effect on the backscattered signals. Target high range resolution radar signatures are transformed into fractals via fractal interpolation techniques, and their fractal dimensions are used to discriminate different targets. The results showed that different target have different targets. The results showed that different target have different fractal dimensions and thus can be discriminated according to their fractal dimensions. High range resolution fully-polarized radar backscattered signals of five aircrafts at different aspects are used to test the algorithm. The classification results presented in this paper are promising. The experiments indicate that the fractal dimension feature used in this paper seems to be independent of amplitude, thus is regarded as a promising new way for radar target classification. It also shows that this opens up an entirely new feature space which needs to be explored further in the field of radar target classification.

关键词： radar target recognition fractal geometry fractal interpolation iterative function system high range resolution polarization

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The Studies of Modeling Method For Three Dimension Iterated Funtion system

The Studies of Modeling Method For Three Dimension Iterated ...

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International Conference on Advances in Materials Science and Information Technologies in Industry (AMSITI)

作者： Dong, Shunsheng Wang, Qian Rong, Xia Liaoning Tech Univ Coll Sci Fuxin 123000 Liaoning Peoples R China Fuxin Coll Coll Sci Fuxin 123000 Liaoning Peoples R China

ISBN: (纸本)9783038350125

In order to describe the shape of the trees in nature better and simulate the trees realistically, This method that by changing the parameters of affine transformation matrix the different types of three dimensional fractal images are drawn is discussed. and the model of generating three dimensional plant is built based on iterated function system. Finally take an example like a set of images through contractive affine transformation and in the chaosPro environment, the graphics are generated and the different types of natural scenery of trees are simulated, using the established model and translation, rotation and scaling of affine transformation.

关键词： Fractal iterative function system affine transformation

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Research on Nondestructive Image Compression Technology Based on Genetic Algorithm

Research on Nondestructive Image Compression Technology Base...

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2nd International Conference on Mechanical Engineering and Green Manufacturing (MEGM 2012)

作者： He, Jie Guo, Hui Wuzhou Univ Dept Comp Sci Wuzhou 543002 Peoples R China Wuzhou Univ Dept Elect & Informat Engn Wuzhou 543002 Peoples R China

ISBN: (纸本)9783037853771

Based on nondestructive and block iteration function the characteristics of the system, and put forward a kind of improved the global optimal solution from similar partition adaptive genetic algorithm is proposed. in the algorithm for the father the searching space of the individual pieces by gay coding method;Definition of father and son of minimum error for the match fitness function;Genetic algorithm is put forward the improvement of the linear adaptive crossover and mutation probability;Take excellent protection strategy choice. The experimental results show that this method in the similar image guarantee the quality and the compression ratio decompression also can obviously reduce compressed time, effectively improve the searching efficiency.

关键词： Nondestructive image compression Genetic algorithm iterative function system Gray code adaptive

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An Improved Fast Fractal Image Coding Algorithm

An Improved Fast Fractal Image Coding Algorithm

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2nd International Conference on Computer Science and Network Technology (ICCSNT)

作者： Tang Guowei Wu Shuang Zhang Yan Northeast Petr Univ Sch Comp & Informat Technol Daqing Heilongjiang Peoples R China

ISBN: (纸本)9781467329644;9781467329637

With the development of the Internet, new requirements are put forward on image compression effect, compression ratio and encoding and decoding time. The principle of fractal coding is novel. It breaks through the traditional entropy boundary theory. Especially its high compression ratio makes the fractal image coding become a hot research point. But this method has the encoding and decoding lopsided problem. Based on the basic principle of fractal image compression, this paper proposes a calculation method which is based on the main diagonal, namely only using the two diagonal data to do mean calculation. Thus not only reduce the data in operation, but also make the time be reduced to a certain degree. The experimental results show that, under the same quality of the image reconstruction, the algorithm makes the encoding and decoding time be greatly reduced

关键词： Fractal Theory Image Compression Fractal Image Coding iterative function system

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An IFS-based fractal discrete fracture network for hydraulic fracture behavior of rock mass

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ENGINEERING GEOLOGY 2023年第1期324卷

作者： Meng, Qingxiang Xue, Haoyu Zhuang, Xiaoying Zhang, Qiang Zhu, Chun He, Benguo Feng, Gan Rabczuk, Timon Hohai Univ Key Lab Minist Educ Geomech & Embankment Engn Nanjing Peoples R China Hohai Univ Res Inst Geotech Engn Nanjing 210098 Jiangsu Peoples R China Tongji Univ Coll Civil Engn Dept Geotech Engn Shanghai Peoples R China Leibniz Univ Hannover Inst Continuum Mech D-30167 Hannover Germany China Inst Water Resources & Hydropower Res Beijing 100048 Peoples R China Northeastern Univ Key Lab Minist Educ Safe Min Deep Met Mines Shenyang 110004 Peoples R China Sichuan Univ Coll Water Resource & Hydropower State Key Lab Hydraul & Mt River Engn Chengdu 610065 Peoples R China Bauhaus Univ Weimar Inst Struct Mech Weimar Germany

The discrete fracture network (DFN) model is applied for fluid flow and transport simulations in fractured rock masses. In this study, a novel two-dimensional fractal DFN generation method was proposed based on the iterative function system (IFS). To achieve the fine mesh for the DFN model, a refinement technique was presented to remove the short edges and small gaps. Subsequently, the zero-thickness flow cohesive element was inserted at the adjacent edge of elements for the hydraulic fracture modeling. The results indicated that the injection pressure of hydraulic fracture had three phases: Sudden increase, rapid drop-off, and stabilization. Compared with the traditional linear DFN model, the injection pressure evolution and fracture propagation of fractal DFN were significantly affected. In addition, the fracture aperture variation was an important factor influencing hydraulic fracturing in the rock mass. Considering the complexity of the hydraulic fracturing process, the effects of mesh sensitivity and fracture aperture size were also analyzed based on two-dimensional simulation results. This study presents a novel 2D DFN model for an accurate description of fracturing and provides a valuable simulation method for hydraulic fracturing.

关键词： Fractal fracture iterative function system Discrete fracture network Hydraulic fracture

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Digital image sampling curve feature extraction using triangle fractal method

Digital image sampling curve feature extraction using triang...

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3rd World Congress on Intelligent Control and Automation

作者： Pang, SN Li, JG Shanghai Jiao Tong Univ Image Proc & Pattern Recognit Inst Shanghai 200030 Peoples R China

ISBN: (纸本)7312012035

Based on the discrete Lyapunov theory, this paper first gives the definition of chaotic curve, then according to the fractal character of such curves iterrative function system.(IFS), which consists of a series of affine transform on triangle basis is designed. So, A triangle fractal feature extraction method is introduced. The result of the experiment indicated the math model we proposed has fast converge speed and can provide rich and accurate features of the curves.

关键词： fractal linear sampling affine transform iterative function system

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