V -variable fractals: Fractals with partial self similarity ✩
V -variable fractals: Fractals with partial self similarity ✩
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DOI：
10.1016/j.aim.2008.04.011
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发表时间：
2008-02
影响因子：
1.7
通讯作者：
M. Barnsley;J. Hutchinson;Orjan Stenflo
中科院分区：
文献类型：
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作者：
M. Barnsley;J. Hutchinson;Orjan Stenflo
建立了一种在所有尺度上都具有部分自相似的新型分形的性质。对于任何具有相关概率分布的迭代函数系统的集合和任何正整数V，都有相应的一类V变量分形集或测度。这些v变量分形也可以由单个确定性迭代函数系统的吸引子上的点得到。在平均收缩假设下，得到了存在唯一性和近似结果。我们还得到了关于迭代函数系统的一些基本结果的推广。
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can also be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.