| 一个3x+1近似推广函数的不动点与分形图像 |
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| 引用本文： | 刘帅,王钲旋. 一个3x+1近似推广函数的不动点与分形图像[J]. 计算机辅助设计与图形学学报, 2009, 21(12) |
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| 作者姓名： | 刘帅 王钲旋 |
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| 作者单位： | 吉林大学计算机科学与技术学院,长春,130021;吉林大学计算机科学与技术学院,长春,130021 |
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| 摘 要： | 为研究以3x+1推广函数T(x)为代表的复指数函数的分形性质,构造了一个3x+1近似推广函数B(x).通过对B(x)的复解析分析,得出了B(x)在实轴和复平面上不动点的性质与求解方法,证明了0点为唯一的吸引不动点;说明了B(x)在复平面上迭代的对称性,求出了函数迭代在整数点处的敛散区域.最后通过绘制函数的分形图像对求得的B(x)分形性质加以验证,同时提出了B(x)收敛域和发散域逐层嵌套的猜想.
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| 关 键 词： | 分形 3x+1推广函数 不动点 复平面 收敛性 发散性 |
Fixed Point and Fractal Images for a Generalized Approximate 3x+1 Function |
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| Liu Shuai,Wang Zhengxuan. Fixed Point and Fractal Images for a Generalized Approximate 3x+1 Function[J]. Journal of Computer-Aided Design & Computer Graphics, 2009, 21(12) |
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| Authors: | Liu Shuai Wang Zhengxuan |
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| Abstract: | In order to study the fractal character of complex exponential functions represented by generalized 3x+1 function T(x),a generalized approximate 3x+1 function B(x) is constructed. With complex analytical analysis for B(x), the fixed points of B(x) at real axis and C-plane are found. It is proved that zero is the only attract fixed point and the iteration of B(x) on the complex plane is symmetrical. And the domains of the constringency and the divergence of B(x) are given. Finally the fractal images are drawn to validate the fractal character of B(x) and a conjecture, which the constringency and the divergence of B(x) is nested, is put forward. |
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| Keywords: | fractal generalized 3x+1 function fixed point C-plane constringency divergence |
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