Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Burrow architecture and digging activity in the Cape dune mole rat

While females are traditionally thought to invest more time and energy into parental care than males, males often invest more resources into searching and displaying for mates, obtaining mates and in male-male conflict. Solitary subterranean mammals perform these activities in a particularly challenging niche, necessitating energetically expensive burrowing to both search for mates and forage for food. This restriction presumably affects males more than females as the former are thought to dig longer tunnels that cover greater distances to search for females. We excavated burrow systems of male and female Cape dune mole rats Bathyergus suillus the, largest truly subterranean mammal, to investigate whether male burrows differ from those of females in ways that reflect mate searching by males. We consider burrow architecture (length, internal dimensions, fractal dimension of tunnel systems, number of nesting chambers and mole mounds on the surface) in relation to mating strategy. Males excavated significantly longer burrow systems with higher fractal dimensions and larger burrow areas than females. Male burrow systems were also significantly farther from one another than females were from other females' burrow systems. However, no sex differences were evident in tunnel cross-sectional area, mass of soil excavated per mound, number of mounds produced per unit burrow length or mass of soil excavated per burrow system. Hence, while males may use their habitat differently from females, they do not appear to differ in the dimensions of the tunnels they create. Thus, exploration and use of the habitat differs between the sexes, which may be a consequence of sex differences in mating behaviour and greater demands for food.

Intermittent and Scale-Invariant Intensity Fluctuations in Hot Coronal Loops

ABSTRACT BODY: To resolve outstanding questions on heating of coronal loops, we study intensity fluctuations in inter-moss portions of active region core loops as observed with AIA/SDO. The 94Å fluctuations (Figure 1) have structure on timescales shorter than radiative and conductive cooling times. Each of several strong 94Å brightenings is followed after ~8 min by a broader peak in the cooler 335Å emission. This indicates that we see emission from the hot component of the 94Å contribution function. No hotter contributions appear, and we conclude that the 94Å intensity can be used as a proxy for energy injection into the loop plasma. The probability density function of the observed 94Å intensity has 'heavy tails' that approach zero more slowly than the tails of a normal distribution. Hence, large fluctuations dominate the behavior of the system. The resulting 'intermittence' is associated with power-law or exponential scaling of the related variables, and these in turn are associated with turbulent phenomena. The intensity plots in Figure 1 resemble multifractal time series, which are common to various forms of turbulent energy dissipation. In these systems a single fractal dimension is insufficient to describe the dynamics and instead there is a spectrum of fractal dimensions that quantify the self-similar properties. Figure 2 shows the multifractal spectrum from our data to be invariant over timescales from 24 s to 6.4 min. We compare these results to outputs from theoretical energy dissipation models based on MHD turbulence, and in some cases we find substantial agreement, in terms of intermittence, multifractality and scale invariance. Figure 1. Time traces of 94A intensity in the inter-moss portions of four AR core loops. Figure 2. Multifractal spectra showing timescale invariance. The four cases of Figure 1 are included.

Evaluation of the Retinal Vasculature in Hypertension and Chronic Kidney Disease in an elderly population of Irish nuns

Background: Chronic kidney disease (CKD) and hypertension are global public health problems associated with considerable morbidity, premature mortality and attendant healthcare costs. Previous studies have highlighted that non-invasive examination of the retinal microcirculation can detect microvascular pathology that is associated with systemic disorders of the circulatory system such as hypertension. We examined the associations between retinal vessel caliber (RVC) and fractal dimension (DF), with both hypertension and CKD in elderly Irish nuns.

Methods: Data from 1233 participants in the cross-sectional observational Irish Nun Eye Study (INES) were assessed from digital photographs with a standardized protocol using computer-assisted software. Multivariate regression analyses were used to assess associations with hypertension and CKD, with adjustment for age, body mass index (BMI), refraction, fellow eye RVC, smoking, alcohol consumption, ischemic heart disease (IHD), cerebrovascular accident (CVA), diabetes and medication use.

Results: In total, 1122 (91%) participants (mean age: 76.3 [range: 56-100] years) had gradable retinal images of sufficient quality for blood vessel assessment. Hypertension was significantly associated with a narrower central retinal arteriolar equivalent (CRAE) in a fully adjusted analysis (P = 0.002; effect size= -2.16 μm; 95% confidence intervals [CI]: -3.51, -0.81 μm). No significant associations between other retinal vascular parameters and hypertension or between any retinal vascular parameters and CKD were found.

Conclusions: Individuals with hypertension have significantly narrower retinal arterioles which may afford an earlier opportunity for tailored prevention and treatment options to optimize the structure and function of the microvasculature, providing additional clinical utility. No significant associations between retinal vascular parameters and CKD were detected.

Gorgonians of the South of Portugal: biology, ecology and conservation

O papel ecológico das gorgónias (Octocorallia: Alcyonacea) nos fundos marinhos rochosos é mundialmente reconhecido. Contudo, a informação acerca da ecologia e biologia das espécies de gorgónias nas zonas temperadas do NE Atlântico é manifestamente escassa, especialmente tendo em consideração as actuais perturbações globais, regionais e locais. Nos fundos rochosos da costa algarvia até aos 30 m, verificouse que várias espécies de gorgónias são abundantes e frequentes, nomeadamente Eunicella labiata, Eunicella gazella, Eunicella verrucosa, Leptogorgia lusitanica e Leptogorgia sarmentosa. As populações de gorgónias são co-dominadas por diferentes espécies que apresentaram elevados índices de associação, indicando reduzidos níveis de competição entre elas. Em todo o caso, a estrutura dos povoamentos diferiu com as condições locais. Todas as espécies evidenciaram padrões de distribuição semelhantes ao longo do gradiente de profundidade, i.e. a abundância aumenta significamente com a profundidade após os 15 m. A profundidades mais baixas (até aos 15 m), a distribuição das gorgónias parece ser condicionada por factores abióticos e pela competição com algas. Com efeito, os padrões de distribuição espacial das espécies de gorgónias na costa algarvia são determinados pela interacção de pressões naturais e antropogénicas (ex. pesca). Ainda que as colónias de maior tamanho não tenham sido restritas a áreas menos pescadas, em áreas mais perturbadas pela pesca, a distribuição dos tamanhos das colónias estava maioritariamente desviada para tamanhos mais pequenos. Os efeitos das perturbações naturais nas populações de gorgónias foram evidenciados pela ocorrência de padrões demográficos distintos em áreas vizinhas sujeitas a níveis semelhantes de pressões antropogénicas. Estes estudos demonstraram, ainda, que os efeitos na distribuição de frequências de tamanho das colónias são dependentes das espécies de gorgónias em causa: Eunicella labiata não parece ser afectada; Leptogorgia sarmentosa é tendencialmente afectada por pressões antropogénicas; Eunicella gazella e Leptogorgia lusitanica aparentam ser afectadas, quer por pressões naturais, quer por pressões antropogénicas. Os efeitos verificados nos padrões da distribuição de frequências de tamanho, particularmente a tendência para o desvio destas frequências para tamanhos mais pequenos em áreas sujeitas a perturbações, poderão ter consequências para a biodiversidade dos fundos sublitorais rochosos na costa algarvia. Com efeito, o presente estudo apoia o paradigma geral de que os corais são habitats que suportam comunidades de elevada biodiversidade e abundância. Num dos poucos estudos que examinam a relação entre as gorgónias e as suas comunidades de invertebrados epibentónicos, foi verificado que as gorgónias (Eunicella gazella e Leptogorgia lusitanica) sustentam comunidades ricas (11 phyla, 181 taxa) e abundantes (7284 indivíduos). Estas comunidades são dominadas por anfípodes, mas os poliquetas tiveram um grande contributo para os níveis elevados de biodiversidade. Verificou-se, igualmente, que o tamanho da colónia desempenha um papel fundamental na biodiversidade, na medida em que as colónias de menor tamanho apresentaram um contributo mais baixo, comparativamente às médias e grandes. Ainda que ambas as gorgónias partilhem a maioria das espécies amostradas, 11 e 18 taxa foram exclusivos de Eunicella gazella e Leptogorgia lusitanica, respectivamente (excluindo indivíduos com presenças únicas). No entanto, a maioria destes taxa eram ou pouco abundantes ou pouco frequentes. A excepção foi a presença de planárias (Turbellaria) de coloração branca nas colónias de Eunicella gazella, provavelmente beneficiando do efeito de camuflagem proporcionado pelos ramos com a mesma coloração. Com efeito, a complementaridade entre as comunidades epibentónicas associadas a ambas as gorgónias diminuiu quando usados os dados de presença/ausência, sugerindo que os padrões de biodiversidade são mais afectados pelas alterações na abundância relativa das espécies dominantes do que pela composição faunística. As comunidades de epifauna bentónica associadas a estas gorgónias não só apresentaram valores elevados de ®-diversidade, como de ¯- diversidade, resultantes de padrões intrincados de variabilidade na sua composição e estrutura. Ainda que o conjunto de espécies disponíveis para colonização seja, na generalidade, o mesmo para ambos os locais, cada colónia apresenta uma parte deste conjunto. Na sua totalidade, as colónias de gorgónias poderão funcionar como uma metacomunidade, mas a estrutura das comunidades associadas a cada colónia (ex. número total de espécies e abundância) parecem depender dos atributos da colónia, nomeadamente superfície disponível para colonização (altura, largura e área), complexidade e heterogeneidade (dimensão fractal e lacunaridade, respectivamente) e cobertura epibentónica “colonial” (ex. fauna colonial e algas macroscópicas; CEC). Numa primeira tentativa para quantificar a relação entre as gorgónias e os invertebrados epibentónicos a elas associados (em termos de abundância e riqueza específica), verificou-se que a natureza e a intensidade destas relações dependem da espécie hospedeira e variam para os grupos taxonómicos principais. No entanto, independentemente do grupo taxonómico, a riqueza específica e a abundância estão significativamente correlacionadas com a CEC. Com efeito, a CEC provavelmente devido a um efeito trófico (aumento da disponibilidade alimentar directo ou indirecto), combinado com a superfície disponível para colonização (efeito espécies-área) foram as variáveis mais relacionadas com os padrões de abundância e riqueza específica. Por outro lado, ainda que a complexidade estrutural seja frequentemente indicada como um dos factores responsáveis pela elevada diversidade e abundância das comunidades bentónicas associadas a corais, a dimensão fractal e a lacunaridade apenas foram relevantes nas comunidades associadas a Leptogorgia lusitanica. A validade do paradigma que defende que a complexidade estrutural promove a biodiversidade poderá ser, então, dependente da escala a que se realizam os estudos. No caso das gorgónias, o efeito da complexidade ao nível dos agregados de gorgónias poderá ser muito mais relevante do que ao nível da colónia individual, reforçando a importância da sua conservação como um todo, por forma a preservar a diversidade de espécies hospedeiras, o seu tamanho e estrutura. Actividades antropogénicas como a pesca, podem, ainda, ter efeitos negativos ao nível da reprodução de espécies marinhas. Analogamente ao verificado para os padrões de distribuição espacial das populações de gorgónias na costa algarvia, a informação relativa à sua reprodução é igualmente escassa. Os estudos realizados em populações de Eunicella gazella a 16m de profundidade, demonstraram que o desenvolvimento anual das estruturas reprodutivas é altamente sincronizado entre os sexos. A razão entre sexos na população foi de 1.09 (F:M), encontrando-se perto da paridade. A espermatogénese estende-se por 6 a 8 meses, enquanto que a oogénese é mais demorada, levando mais de um ano para que os oócitos se desenvolvam até estarem maduros. Antes da libertação dos gâmetas, foi observada uma elevada fecundidade nas fêmeas (27.30§13.24 oócitos pólipo−1) e nos machos (49.30§31.14 sacos espermáticos pólipo−1). Estes valores encontram-se entre os mais elevados reportados à data para zonas temperadas. A libertação dos gâmetas (não há evidência de desenvolvimento larvar, nem à superfície da colónia, nem no seu interior) occorre em Setembro/ Outubro, após um período de elevada temperatura da água do mar. As fêmeas emitem oócitos maduros de elevadas dimensões, retendo, todavia, os oócitos imaturos que se desenvolvem apenas na época seguinte. Ainda que o efeito da pesca nas populações de gorgónias da costa do Algarve seja perceptível, às taxas actuais, o mergulho recreativo não aparenta afectar seriamente estas populações. Contudo, sendo uma indústria em expansão e conhecendo-se a preferência de mergulhadores por áreas rochosas naturais ricas em espécies bentónicas, futuramente poderá vir a afectar estes habitats. A monitorização de mergulhadores na costa algarvia mostrou que a sua maioria (88.6 %) apresenta comportamentos que podem impactar o habitat, com uma taxa média de contactos de 0.340§0.028 contactos min−1. Esta taxa foi mais elevada em mergulhadores com moderada experiência e na fase inicial do mergulho (0–10 min). Os contactos com as barbatanas e mãos foram comuns, resultando, maioritariamente, na resuspensão do sedimento, mas geralmente apresentando um impacto reduzido. Todavia, a fauna também foi afectada, quer por danos físicos, quer pela interacção com os mergulhadores, e num cenário de expansão significativa desta actividade, os impactos na fauna local poderão aumentar, com consequências para os ecossistemas de fundos rochosos da costa sul de Portugal. Na sua globalidade, a informação recolhida nos estudos que contemplam esta tese, por ser em grande parte totalmente nova para a região, espera-se que contribua para a gestão da zona costeira do Algarve.

Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

Complex evolution of a multi-particle system

This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.

Analysis of the respiratory dynamics during normal breathing by means of pseudo phase plots and pressure-volume loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure–volume curves and the pseudophaseplane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Accessing complexity from genome information

This paper studies the information content of the chromosomes of 24 species. In a first phase, a scheme inspired in dynamical system state space representation is developed. For each chromosome the state space dynamical evolution is shed into a two dimensional chart. The plots are then analyzed and characterized in the perspective of fractal dimension. This information is integrated in two measures of the species’ complexity addressing its average and variability. The results are in close accordance with phylogenetics pointing quantitative aspects of the species’ genomic complexity.

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

Analysis of the Respiratory Dynamics During Normal Breathing by Means of Pseudophase Plots and Pressure–Volume Loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure-volume curves and the pseudophase-plane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Synthèse et caractérisation physicochimique de peptides de polyglutamines

Neuf maladies neurodégénératives sont le produit de l’expression de gènes mutés, dans lesquels le codon CAG est répété au-delà d’un seuil pathologique. Ceci produit des protéines mutantes dans lesquelles sont insérés des segments de polyglutamines (polyGln), qui perdent leur activité et acquièrent une nouvelle fonction, ce qui est toxique pour le neurone. Ces altérations sont attribuables aux propriétés particulières de la polyGln. En effet, ces dernières possèdent la capacité de s’assembler pour former des corps d’inclusion intracellulaires. Cette propension à l’agrégation de la polyGln rend difficile l’étude de ces pathologies. C’est ainsi que l’utilisation de peptides peut s’avérer une approche avantageuse. Toutefois, la synthèse de polyGln est associée à de nombreuses délétions et nécessite l’ajout de groupements chargés afin de permettre leur purification. Cependant, ce prérequis donne lieu à des interactions électrostatiques qui biaisent la structure et la cinétique d’agrégation de ces peptides, en plus d’interférer avec l’évaluation d’éventuels agents thérapeutiques. L’objectif du projet est de développer un système permettant l’étude de la polyGln en s’affranchissant des effets de charges. Pour ce faire, deux approches ont été explorées, la première utilise la polyGln non chargée et la seconde utilise une structure polyGln-morpholine ayant des charges labiles en fonction du pH. Ces peptides ont été produits en utilisant une approche linéaire de synthèse peptidique sur support solide avec protection maximale des chaînes latérales. La purification a été effectuée par chromatographie de haute performance en phase inverse en milieu acide. Ces stratégies ont permis de produire des peptides de polyGln de grande pureté avec des rendements acceptables. Une procédure de solubilisation des peptides alliant sonication et lyophilisation a été développée afin d’étudier chacun de ces peptides à l’aide de diverses techniques physicochimiques, telles que la diffusion de la lumière, la spectroscopie de résonance magnétique nucléaire, Raman et UV-visible, le dichroïsme circulaire et la microscopie optique polarisée. La polyGln non chargée solubilisée dans le trifluoroéthanol-eau a montré que la taille des particules et la vitesse d’agrégation sont proportionnelles à la fraction volumique en eau. De plus, la structure secondaire en solution est à prédominance alpha et semble être peu sensible à la fraction d’eau jusqu’à un certain seuil (25%) après lequel la structure aléatoire prédomine. L’analyse des agrégats à l’état solide montre des structures hélicoïdales > aléatoires et ont les caractéristiques des fibrilles amyloïdes. Le peptide de polyGln-morpholines a un pKa de 7,3 en milieu aqueux. Il demeure en solution lorsque le pH < pKa et à faible force ionique, alors qu’il s’autoassemble lorsque ces conditions ne sont pas respectées. Ceci suggère que la répulsion électrostatique est responsable de la stabilisation du peptide en solution. La dimension fractale nous indique que le peptide forme des agrégats compacts dont les constituants ont une taille de 2,5 nm, compatibles avec une conformation aléatoire compacte, en coude bêta ou hélicoïdale. Ceci est en accord avec l’étude structurale des peptides en solution qui a montré des espèces aléatoires > bêta > alpha. De plus, en RMN, l’élargissement des signaux du 1Hγ en cours d’agrégation suggère une interaction via les chaînes latérales. Les analyses en phase solide ont plutôt montré une prédominance de structures bêta et alpha. L’inhibition de l’agrégation à pH 8 varie selon rouge de Congo > tréhalose, alors que le peptide liant la polyGln 1 et la thioflavine T ne semble pas avoir d’effet. Ces approches ont donc permis pour la première fois de s’affranchir des effets de charges auparavant inhérents à l’étude de la polyGln en solution et par conséquent d’obtenir des informations inédites quant à la solubilité, la structure et la cinétique d’agrégation. Enfin, le dispositif à charges labiles permet d’évaluer l’efficacité d’éventuels agents thérapeutiques à pH quasi physiologique.

Geometric characterization of red blood cells. Differentiation of normal and pathologic samples

Introduction. Fractal geometry measures the irregularity of abstract and natural objects with the fractal dimension. Fractal calculations have been applied to the structures of the human body and to quantifications in physiology from the theory of dynamic systems.Material and Methods. The fractal dimensions were calculated, the number of occupation spaces in the space border of box counting and the area of two red blood cells groups, 7 normal ones, group A, and 7 abnormal, group B, coming from patient and of bags for transfusion, were calculated using the method of box counting and a software developed for such effect. The obtained measures were compared, looking for differences between normal and abnormal red blood cells, with the purpose of differentiating samples.Results. The abnormality characterizes by a number of squares of occupation of the fractal space greater or equal to 180; values of areas between 25.117 and 33.548 correspond to normality. In case that the evaluation according to the number of pictures is of normality, must be confirmed with the value of the area applied to adjacent red blood cells within the sample, that in case of having values by outside established and/or the greater or equal spaces to 180, they suggest abnormality of the sample.Conclusions. The developed methodology is effective to differentiate the red globules alterations and probably useful in the analysis of bags of transfusion for clinical use 

Descripción matemática con dimensiones fractales de células normales y con anormalidades citológicas de cuello uterino

Introducción. La geometría fractal ha mostrado ser adecuada en la descripción matemática de objetos irregulares; esta medida se ha denominado dimensión fractal. La aplicación del análisis fractal para medir los contornos de las células normales así como aquellas que presentan algún tipo de anormalidad, ha mostrado la posibilidad de caracterización matemática de su irregularidad. Objetivos. Medir, a partir de la geometría fractal células del epitelio escamoso de cuello uterino clasificadas como normales, atipias escamosas de significado indeterminado (ASC-US) y lesiones intraepiteliales escamosas de bajo grado (LEIBG), diagnosticadas mediante observación microscópica, en busca de mediciones matemáticas que las distingan. Metodología. Este es un estudio exploratorio descriptivo en el que se calcularon las dimensiones fractales, con el método de box counting simplificado y convencional, de los contornos celular y nuclear de 13 células del epitelio escamoso de cuello uterino normales y con anormalidades como ASC-US y lesiones intraepiteliales de bajo grado (LEI BG), a partir de fotografías digitales de 7 células normales, 2 ASCUS y 4 LEI BG diagnosticadas con criterios citomorfológicos mediante observación microscópica convencional. Resultados. Se desarrolló una medida cuantitativa, objetiva y reproducible del grado de irregularidad en las células del epitelio escamoso de cuello uterino identificadas microscópicamente como normales, ASC-US y LEI BG. Conclusiones Se evidenció una organización fractal en la arquitectura celular normal, así como en células ASC-US y las lesiones intraepiteliales de bajo grado (LEI BG). No se encontraron diferencias entre los tipos celulares estudiados.

The population genetic structure of clonal organisms generated by exponentially bounded and fat-tailed dispersal

Long distance dispersal (LDD) plays an important role in many population processes like colonization, range expansion, and epidemics. LDD of small particles like fungal spores is often a result of turbulent wind dispersal and is best described by functions with power-law behavior in the tails ("fat tailed"). The influence of fat-tailed LDD on population genetic structure is reported in this article. In computer simulations, the population structure generated by power-law dispersal with exponents in the range of -2 to -1, in distinct contrast to that generated by exponential dispersal, has a fractal structure. As the power-law exponent becomes smaller, the distribution of individual genotypes becomes more self-similar at different scales. Common statistics like G(ST) are not well suited to summarizing differences between the population genetic structures. Instead, fractal and self-similarity statistics demonstrated differences in structure arising from fat-tailed and exponential dispersal. When dispersal is fat tailed, a log-log plot of the Simpson index against distance between subpopulations has an approximately constant gradient over a large range of spatial scales. The fractal dimension D-2 is linearly inversely related to the power-law exponent, with a slope of similar to -2. In a large simulation arena, fat-tailed LDD allows colonization of the entire space by all genotypes whereas exponentially bounded dispersal eventually confines all descendants of a single clonal lineage to a relatively small area.