摘要
对所建立的菊花石生长模型进行了详细的数理分析．菊花石生长模型具分形特点，其豪斯道夫维数为：１＜Ｄ＜１＋ｌｎ２／ｌｎ（２β）（β≥１），说明菊花石形态不同于一维柱体（虽然它是由柱体放射状集合而成），也不同于三维球体（虽然它是一个似球状的花体）；Ｄ同时还蕴含着结晶行为上的物理意义，即Ｄ＝１时无分叉成核行为，Ｄ＞１时有分叉成核行为，且Ｄ越大分叉成核越多；无核生长比有核生长的Ｄ大等等．本模型的Ｄ在１～１＋ｌｎ２／ｌｎ（２β）（β≥１）之间的多变性可与多重分形类比，且可与扩散限制聚集（ＤＬＡ）模型周界点集的多分维特点类比．
The theoretic analysis of the growth model of the chrysanthemum stone has been made. The model is of fractal feature and its Hausdorff dimension is: 1<D<1+ ln 2/ ln (2β)(β≥1). Such a model shows the morphology of the chrysanthemum stone is different not only from one_dimensional column (although it is composed of many radiated columns), but also from three_dimensional globe (although it looks like a globular flower). D has also the implication of the crystallization behavior: D=1 indicates that there is not any divaricating nucleation, D>1 indicates that there is divaricating nucleation and the larger D , the more divaricating nucleation. The D of no nucleus_growth model is larger than that of nucleus_growth model, etc.. This variety of the D between 1～1+ ln 2/ ln (2β)(β≥1) is similar to a multi_fractal, and also similar to the feature of multi_fractal_dimension of the DLA model's boundary point sets.
出处
《地球科学（中国地质大学学报）》
EI
CAS
CSCD
北大核心
1999年第1期69-73,共5页
Earth Science-Journal of China University of Geosciences
基金
国家自然科学基金
