| 王兴元,骆超.一个非解析复映射的广义Mandelbrot集[J].,2009,(1):128-132 |
| 一个非解析复映射的广义Mandelbrot集 |
| Generalized Mandelbrot sets from a nonanalytic complex mapping |
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| DOI：10.7511/dllgxb200901024 |
| 中文关键词: 非解析映射 广义M集 分形 演化 |
| 英文关键词: nonanalytic mapping generalized Mandelbrot sets fractal evolution |
| 基金项目:国家自然科学基金资助项目(60573172)；高等学校博士学科点专项科研基金资助项目(20070141014)；辽宁省自然科学基金资助项目(20082165) |
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| 中文摘要: |
| 推广了Michelitsch等所提出的由一个简单非解析映射构造Mandelbrot集的方法，并由推广的复映射，构造出一系列实数阶的广义Mandelbrot集(简称广义M集)．利用复变函数理论和计算机制图相结合的实验数学方法，对广义M集的结构和演化进行了研究．结果表明 广义M集的几何结构依赖于参数\%α和R；\%整数阶广义M集具有对称性和分形特征；小数阶广义M集出现了错动和断裂，且其演化过程依赖于相角主值范围的选取． |
| 英文摘要: |
| The method constructing the Mandelbrot sets from a simple nonanalytic mapping developed by Michelitsch, \%et al.\% was expanded. According to the expanded complex mapping, a series of the generalized Mandelbrot sets for real index number were constructed. Using the experimental mathematical method combining the theory of analytic function of one complex variable with computer-aided drawing, the fractal features and evolutions of the generalized Mandelbrot sets were studied. The results show the following facts: the geometry structure of the generalized Mandelbrot sets depends on the parameters of α and R ; the generalized Mandelbrot sets for integer index number have symmetry and fractal feature; the generalized Mandelbrot sets for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle. |
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