Pointwise Dimension Analyses of the Las Campanas Redshift Survey

最简单地说，宇宙学的基本目标之一就是尽可能准确地描述宇宙。为了做到这一点，宇宙的多个方面，无论是过去的还是现在的，必须完全建模。其中一些特征包括宇宙及其组成部分的年龄、密度、温度和范围。即将开展的研究将探索宇宙中物体的集群。用本努瓦·曼德布洛特的这句名言来概括现代的分形几何学的动机可能是最好的：“山不是圆锥体，云不是球体，海岸线不是圆，树皮也不光滑，闪电也不是直线传播的。”用最简单的话说，分形图是“在所有尺度上(大致)自相似的物体”。现代社会对分形学重新燃起了兴趣，将其应用于宇宙大尺度结构的研究，为早在20世纪20年代C.V.L.Charlier绘制的河外星云图就已经定性表达的概念提供了一种定量描述方案。拉斯坎帕纳斯红移调查，大约有26000个星系，有关于星系的位置和红移信息，这些数据将使用逐点维度或PD方法进行研究。PD方法是一种易于使用的分形统计量，与用于研究星系团的更传统方法相比，它具有许多优势。人们希望能够收集到更多关于拉斯坎帕纳斯星表中星系环境的信息，这些结果可以用来比较未来星表的研究结果。***

AST-9808608 Best In simplest terms, one of the fundamental goals of cosmology is to describe the Universe as accurately as possible. In order to do this, the multiple aspects of the Universe, both past and present-day, must be completely modeled. Some of these characteristics include the age, density, temperature, and extent of the Universe and its components. The research to be carried out will explore the clustering of objects in the Universe. The modern motivation for fractal geometry may best be summed up by this quote of Benoit Mandelbrot: "Mountains are not cones, clouds are not spheres, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." Fractals are, in simplest terms, "objects which are (approximately) self-similar on all scales". The renewed modern interest in fractals has led to applying it to the study of large-scale structure in the Universe, giving a quantitative descriptive scheme to ideas that had been expressed qualitatively as early as C. V. L. Charlier's map of extragalactic nebulae in the 1920s. The Las Campanas Redshift Survey, of about 26000 galaxies, has positional and redshift information on the galaxies and these data will be studied using the pointwise dimension, or PD method. The PD method is an easy-to-use fractal statistic which has numerous advantages over the more traditional methods used to study the clustering of galaxies. It is hoped that much information can be gleaned about the environments of the galaxies in the Las Campanas catalog and these results may be used for comparison of results of studies of future catalogs. ***