植被格局的分形模型：植被格局的分形特征

 目前植被格局研究存在一些问题,分形模型是解决这些问题的有力工具。选择从分枝到景观的各个等级层次上若干有代表性的研究实例进行介绍,给出了尺度、自相似性和分形维数在植被格局研究中的应用方法,说明了分形模型描述植被格局的实用性和优越性。在此基础上提出植被格局的分形机制,认为植被格局是具有自组织特征的分形体。最后对植被格局的分形模型进行了评价,提出研究中需要注意的若干问题以及未来的发展方向。     

分形及其在植物研究中的应用

本文着重介绍了非线性科学热点之一的分形理论,并综述了分形理论在植物结构模拟、植物群落研究、景观格局研究、树木冠层特征研究、木材学研究、作物根系研究等方面的应用进展以及分维数求算方法研究进展,最后,对非线性理论在植物研究领域应用前景进行了展望。     

Fractal dimension of humic acids

Small-angle neutron scattering experiments have been made on solutions of humic acid aggregates with an acidity corresponding to pH 5.0 and at 0.1 M ionic strength. We observe power-law decay of the intensity over one decade of the scattering vector, Q, indicating that the aggregates are fractal. We explain the normalized intensity in the entire Q-range by assuming that the humic acid particles can be described by building units of a radial size, 25 Å, aggregated into clusters with an average radius of 400–500 Å. For humic acids obtained from two different sources, we determine the fractal dimension, D = 2.3 ± 0.1. For small values of Q, the measured data of one of the samples extend into the Guinier range giving an average radius of gyration of 320 ± 20 Å. Correspondence to: R. Österberg     

Cellular “bauplans”: Evolving unicellular forms by means of Julia sets and Pickover biomorphs

The universe of cellular forms has received scarce attention by mainstream neo-Darwinian views. The possibility that a fundamental trait of biological order may consist upon, or be guided by, developmental processes not completely amenable to natural selection was more akin to previous epochs of biological thought, i.e. the “bauplan” discussion. Thirty years ago, however, Lynn and Tucker studied the biological mechanisms responsible for defining organelles position inside cells. The fact that differentiated structures performing a specific function within the eukaryotic cell (i.e. mitochondrion, vacuole, or chloroplast) were occupying specific positions in the protoplasm was the observational and experimental support of the ‘morphogenetic field’ notion at the cellular level. In the present paper we study the morphogenetic field evolution yielding from an initial population of undifferentiated cells to diversified unicellular organisms as well as specialized eukaryotic cell types. The cells are represented as Julia sets and Pickover biomorphs, simulating the effect of Darwinian natural selection with a simple genetic algorithm. The morphogenetic field “defines” the locations where cells are differentiated or sub-cellular components (or organelles) become organized. It may be realized by different possibilities, one of them by diffusing chemicals along the Turing model. We found that Pickover cells show a higher diversity of size and form than those populations evolved as Julia sets. Another novelty is the way that cellular organelles and cell nucleus fill in the cell, always in dependence on the previous cell definition as Julia set or Pickover biomorph. Our findings support the existence of specific attractors representing the functional and stable form of a differentiated cell—genuine cellular bauplans. The configuration of the morphogenetic field is “attracted” towards one or another attractor depending on the environmental influences as modeled by a particular fitness function. The model promotes the classical discussions of D’Arcy Thompson and the more recent views of Waddington, Goodwin and others that consider organisms as dynamical systems that evolve through a ‘master plan’ of transformations, amenable to natural selection. Intriguingly, the model also connects with current developments on mechanobiology, highlighting the informational–developmental role that cytoskeletons may play.     

Fractal properties of forest spatial structure

The definition of fractal dimension of natural objects, which enables to deal with scale dependence of fractal dimension is discussed. Abrupt changes of fractal dimension of spatial structure of terrestrial ecosystems are considered in the context of hierarchical paradigm. On this ground the procedure is proposed for segmentation of a territory, which takes into account the scale dependence of spatial variability of ecological parameters. Using remotely sensed data — normalized difference vegetation index (NDVI) and thermal radiation in the infrared band — fractal dimensions and critical scales are evaluated for different forest types with the help of software, developed for this purpose. The results obtained corroborate the potentialities of fractal approach in ecology. These methods and results can be used for discrimination of remotely sensed data; but further investigations, including detailed comparison of fractal characteristics of remotely sensed forest images with results of on-site field studies are necessary to validate them.     

桂花叶片的分形特征

提供了一种叶片分形维数的测定方法,并用其测定了桂花(Osmanthus fragrans Lour)的叶片分形维数。通过分析发现：(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。     

Fractal spreading growth of Serratia marcescens which produces surface active exolipids

An irregular fiord-like outline of a S. marcescens colony expanding on a hard agar medium was shown to be fractal which promised an extremely long array of outermost cells. For the analysis of such spreading growth, mutants defective in production of surface active exolipids (serawettin W1 and W3) and flagella-less mutants were isolated. The fractal spreading growth was found to be correlated with serrawettin production. Furthermore, serrawettin-less mutants demonstrated spreading growth when purified serrawettin W1 or W3 were supplied exogenously.     

Fractal dimension of birds population sizes time series

Information about fractal dimension is collected so that it can be applied to time series interpreting Hurst coefficient. The population size of a species is modelled as a dynamic system. The Hurst coefficient is calculated for these times series. A computer programme has been elaborated to compute the Hurst exponent of time series using the algorithms of range increment, second order moment increment and local second order moment increment. It has been applied to time series of birds' populations.     

羊草种群地上部生物量与株高的分形关系

应用分形几何学（Ｆｒａｃｔａｌ ｇｅｏｍｅｔｒｙ）的原理和方法对羊草（Ａｎｅｕｒｏｌｅｐｉｄｉｕｍ ｃｈｉ－ ｎｅｎｓｅ）种群地上部生物量与株高的关系进行了研究．结果表明．羊草种群的地上部生物量 与株高存在很好的静态分形关系,所得分形维数是对地上部生物量在各器官中积累规律 （生物量配比）的表征;羊草种群地上部生物量与株高的动态分形关系表明在整个生长季 内该种群地上部生物量的增长具有自相似性．是一个分形生长过程,增长规律为分形维数 值Ｄ;在此基础上建立了羊草种群的分形生长模式．认为成熟植株可以看作是其幼苗经生 长放大过程而得到的．     

Spectral and Fractal Analysis of Cerebellar Activity After Single and Repeated Brain Injury

The cerebellum, even when not directly damaged, is potentially interesting for understanding the adaptive responses to brain injury. Cerebellar electrocortical activity (ECoG) in rats was studied using spectral and fractal analysis after single and repeated unilateral injury of the parietal cortex. Local field potentials of cerebellar paravermal cortex were recorded before brain injury, in the acute phase (up to 2.5 hours) after a first injury of anesthetized rats, and then before and after second, third, and, in some cases, fourth injury. Relative gamma power (32.1–128.0 Hz) and fractal dimension of ECoGs were temporarily increased after the first injury. However, there was a permanent mild increase in gamma activity and a mild increase in the fractal dimension of cerebellar activity as a chronic change after repeated remote brain injury. There was a negative linear correlation between the normalized difference in fractal dimensions and normalized difference in gamma powers of cerebellar activity only in the case of repeated brain injury. This is the first study showing that correlation between the parameters of spectral and fractal analyses of cerebellar activity can discriminate between single and repeated brain injuries, and is, therefore, a promising approach for identifying specific pathophysiological states.