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Journal articles on the topic 'Leaf fractal dimensions'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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1

Lapinig, Vincent T., Celso C. Almirol, Anna Lou C. Cabuenas, and Mc Nell O. Sabandal. "Classification of mangrove species based on leaf fractal dimensions." University of the Visayas - Journal of Research 7, no. 1 (2013): 25–34. https://doi.org/10.5281/zenodo.1620305.

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 The study utilized the fractal dimensions of the leaves of mangrove species locally found in the City of Tangub to determine if the same can be used for classification purposes. The species used were: Rhizophora mucronata, Avicennia marina, Pemphis acidula, Sonneratia alba and Acrostichum aureum. Findings revealed that fractal dimensions can be used to differentiate one mangrove species from another through their leaf roughness (f =14.400, p = 0.000). However, leaf fractal dimensions alone cannot differentiate the following mangrove species within groups: {Rhizopora mucronata and Avicenn
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2

Vlcek, J., and E. Cheung. "Fractal analysis of leaf shapes." Canadian Journal of Forest Research 16, no. 1 (1986): 124–27. http://dx.doi.org/10.1139/x86-020.

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An application of fractal mathematics to the analysis of leaf shapes is presented. Six leaves randomly selected from nine tree species were used in the study. A video imaging method together with microcomputer-based image processing was used to generate leaf outlines. A fractal analysis program was written to calculate the fractal dimensions of the leaves. Recalling a leaf outline from a diskette and specifying both the starting position on it (e.g., the beginning of the petiole) and six step lengths (explained later), the program then generates the fractal dimension according to the theory de
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3

Almirol, Celso, Vincent Lapinig, and Mc Nell Sabandal. "Classification of Marine Seagrasses by Leaf Fractal Dimensions Analysis." Recoletos Multidisciplinary Research Journal 1, no. 2 (2013): 159–66. http://dx.doi.org/10.32871/rmrj1301.02.18.

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4

Bagchi, Debjani, Avik Dasgupta, Amit D. Gondaliya, and Kishore S. Rajput. "Insights from the Plant World: A Fractal Analysis Approach to Tune Mechanical Rigidity of Scaffolding Matrix in Thin Films." Advanced Materials Research 1141 (August 2016): 57–64. http://dx.doi.org/10.4028/www.scientific.net/amr.1141.57.

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Using a fractal analysis approach to study plant leaf venation and stem sections, we find that plants use very intelligent scaffolding strategies to tune mechanical strength of leaves and stems. Within plant organs, specialized types of tissues with different mechanical properties have evolved. Ideally, the biopolymers cellulose, hemicelluloses and lignin present in plant cell walls confer mechanical rigidity to plant tissues, but our studies reveal that the manner these biopolymers are distributed in the tissue matrix hold the key to the mechanical rigidity of the tissues. We have developed a
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5

Dobrei, Alin, and Florin Sala. "Multivariate analysis in grapevine genotypes based on fractal dimensions." JOURNAL OF HORTICULTURE, FORESTRY AND BIOTECHNOLOGY 29, no. 1 (2025): 48–57. https://doi.org/10.59463/1ep6tr22.

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Multivariate analysis was used to study some grapevine genotypes based on fractal parameters of leaf geometry. The following grapevine genotypes were studied: 'Cabernet Sauvignon' (CS), 'Chasselas' (Ch), 'Muscat Hamburg' (MH), 'Muscat Iantarnîi' (MI), 'Muscat Ottonel' (MO), 'Perlă de Csaba' (PC), and 'Victoria' (Vi). A flowchart diagram was generated by the authors, which included the work steps in relation to the purpose of the study. The data series represented a normal distribution. According to the multivariate analysis, fractal parameters loaded differentially on the principal components.
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6

Borkowski, Wojciech. "Fractal dimension based features are useful descriptors of leaf complexity and shape." Canadian Journal of Forest Research 29, no. 9 (1999): 1301–10. http://dx.doi.org/10.1139/x99-112.

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An application of fractal dimensions as measures of leaf complexity to morphometric studies and automated plant identification is presented. Detailed algorithms for the calculation of compass dimension and averaged mass dimension together with a simple method of grasping the scale range related variability are given. An analysis of complexity of more than 300 leaves from 10 tree species is reported. Several classical biometric descriptors as well as 16 fractal dimension features were computed on digitized leaf silhouettes. It is demonstrated that properly defined fractal dimension based featur
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7

Juwitarty, Novita Anggraini, Kosala Dwidja Purnomo, and Kiswara Agung Santoso. "PENDETEKSIAN CITRA DAUN TANAMAN MENGGUNAKAN METODE BOX COUNTING." Majalah Ilmiah Matematika dan Statistika 20, no. 1 (2020): 35. http://dx.doi.org/10.19184/mims.v20i1.17221.

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Different types of plants make identification difficult. Therefore, we need a system that can identify the similarity of the leaves based on a reference leaf. Extraction can be done by taking one part of the plant and the most easily obtained part is the leaf part. Natural objects such as leaves have irregular shapes and are difficult to measure, but this can be overcome by using fractal dimensions. In this research, image detection of plant leaves will be carried out using the box counting method. The box counting method is a method of calculating fractal dimensions by dividing images into sm
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8

BOUDON, FRÉDÉRIC, CHRISTOPHE GODIN, CHRISTOPHE PRADAL, OLIVIER PUECH, and HERVÉ SINOQUET. "ESTIMATING THE FRACTAL DIMENSION OF PLANTS USING THE TWO-SURFACE METHOD: AN ANALYSIS BASED ON 3D-DIGITIZED TREE FOLIAGE." Fractals 14, no. 03 (2006): 149–63. http://dx.doi.org/10.1142/s0218348x06003179.

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In this paper, we present a method to estimate the fractal dimension of plant foliage in three dimensions (3D). This method is derived from the two-surface method introduced in the 90s to estimate the fractal dimension of tree species from field measurements on collections of trees. Here we adapted the method to individual plants. The multiscale topology and geometry of the plant must first be digitized in 3D. Then leafy branching systems of different sizes are constructed from the plant database, using the topological information. 3D convex envelops are then computed for each leafy branching
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9

Rani, Rudrama Kodali, Siddaiah Polepalli, and Nanjappa Giri Prasad Mahendra. "Bandwidth enhanced deltoid leaf fractal antenna for 5.8 GHz WLAN applications." TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 20, no. 5 (2022): 963–70. https://doi.org/10.12928/telkomnika.v20i5.23489.

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A wideband deltoid leaf fractal antenna is proposed for 5.8 GHz commonly used in industrial scientific and medical (ISM) and wireless local area networks (WLAN) applications. A microstrip patch antennas is designed with leaf shape radiating element. Using a leaf shape, it is possible to increase the perimeter of a design and thus reduce the overall dimensions of the antenna. A circular ring slot is made on the leaf shaped radiator, in a way that a circular disc is loaded at centre. Triangular fractal slots are made inside the circular disc to make it miniaturized. A partial ground is maintaine
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10

Bayirli, Mehmet, Selami Selvi, and Ugur Cakilcioglu. "Determining different plant leaves’ fractal dimensions: a new approach to taxonomical study of plants." Bangladesh Journal of Botany 43, no. 3 (2015): 267–75. http://dx.doi.org/10.3329/bjb.v43i3.21593.

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Fractal dimensions of leaves from Cercis canadensis L., Robinia pseudoacacia L., Amelanchier arborea (F.Michx.) Fernald, Prunus persica (L.) Batsch, Quercus alba L., Carpinus caroliniana Walter, Ficus carica L., Morus rubra L., Platanus orientalis L., and Ulmus rubra Muhl. were calculated. The values were then confirmed and compared by those obtained from box-counting method and the exponent values of densitydensity correlation function (first time in the literature). It is now proposed for the first time that there is a relationship between a fractal dimension of the leaf and a surface densit
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11

Chen, An Qiang, Gang Cai Liu, and Dan Zhang. "A Study on the Relationship between Crown Characteristics, Fractal Dimension and Water Consumption of Poplars." Advanced Materials Research 255-260 (May 2011): 2919–24. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2919.

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The relationships among crown characteristics, crown fractal dimensions and water consumption were studied in seven 5-year-old poplar clones that were selected from the nursery garden of the Gaomi Forestry Bureau in China. The closest positive correlation was between single tree leaf area (TLA) and water consumption followed by the tree crown area (TCA). The leaf area index (LAI) and crown layer density (CLD) were positively correlated with water consumption but were not significantly correlated. There was a negative correlation between the crown shape ratio (CSR) of the L35, NL895 and I-107 p
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12

Tariq, Muhammad Hamza, Haseeb Sultan, Rehan Akram, et al. "Estimation of Fractal Dimensions and Classification of Plant Disease with Complex Backgrounds." Fractal and Fractional 9, no. 5 (2025): 315. https://doi.org/10.3390/fractalfract9050315.

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Accurate classification of plant disease by farming robot cameras can increase crop yield and reduce unnecessary agricultural chemicals, which is a fundamental task in the field of sustainable and precision agriculture. However, until now, disease classification has mostly been performed by manual methods, such as visual inspection, which are labor-intensive and often lead to misclassification of disease types. Therefore, previous studies have proposed disease classification methods based on machine learning or deep learning techniques; however, most did not consider real-world plant images wi
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13

Osawa, Akira. "Inverse relationship of crown fractal dimension to self-thinning exponent of tree populations: a hypothesis." Canadian Journal of Forest Research 25, no. 10 (1995): 1608–17. http://dx.doi.org/10.1139/x95-175.

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The self-thinning rule describes in overcrowded even-aged plant monocultures a consistent relationship of mean mass to the approximately −3/2 power of plant density. Recent analyses revealed cases of statistically significant departures of the exponent from −3/2, confirming earlier suggestions. Shade tolerance, crown structure, and stand conditions have been suggested to influence variation in the self-thinning exponent; however, quantitative relationships of the species' traits to thinning exponent have been unclear. I examined patterns of crown fractal dimension, a quantitative measure of cr
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14

Guo, Fei-Yan, Jia-Jun Zhou, Zhong-Yuan Ruan, Jian Zhang, and Lin Qi. "Hub-collision avoidance and leaf-node options algorithm for fractal dimension and renormalization of complex networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (2022): 123116. http://dx.doi.org/10.1063/5.0113001.

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The box-covering method plays a fundamental role in the fractal property recognition and renormalization analysis of complex networks. This study proposes the hub-collision avoidance and leaf-node options (HALO) algorithm. In the box sampling process, a forward sampling rule (for avoiding hub collisions) and a reverse sampling rule (for preferentially selecting leaf nodes) are determined for bidirectional network traversal to reduce the randomness of sampling. In the box selection process, the larger necessary boxes are preferentially selected to join the solution by continuously removing smal
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15

Li, Annan, and Na Fu. "The construction of a smallholder credit evaluation system based on biomechanical characteristics: A synergistic analysis of crop growth potential and risk management." Molecular & Cellular Biomechanics 22, no. 4 (2025): 908. https://doi.org/10.62617/mcb908.

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This study proposes an innovative credit evaluation system for small-scale farmers by integrating biomechanical characteristics analysis with traditional credit assessment methods. Through the Analytic Hierarchy Process (AHP), we develop a comprehensive evaluation framework encompassing five dimensions: farmers’ personal characteristics, solvency, credit status, loan guarantee, and production operations. The research introduces a novel biomechanics-driven credit risk assessment model (BICAM) that establishes quantitative relationships between plant mechanical properties and agricultural manage
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16

Zhang, Ruhua, and Wei Xiao. "What is the variant of fractal dimension under addition of functions with same dimension and related discussions." AIMS Mathematics 9, no. 7 (2024): 19261–75. http://dx.doi.org/10.3934/math.2024938.

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<abstract><p>This paper attempts to explore possible box dimension of two added fractal continuous functions with the same dimension. Two interesting and meaningful results are obtained. Let $ g(x) $ and $ h(x) $ have the same box dimension $ t\; (1 < t\leq 2) $, the box dimension of $ g(x)+h(x) $ may or may not exist. If it exists, it can take an arbitrary real number $ \gamma $ satisfying $ 1 < \gamma\leq t $. If it does not exist, its lower and upper box dimensions can reach arbitrary different real numbers $ t_1\; {\rm and}\; t_2 $ that satisfy $ 1 < t_1 &a
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17

Muchtar, Mutmainnah, Nanik Suciati, and Chastine Fatichah. "FRACTAL DIMENSION AND LACUNARITY COMBINATION FOR PLANT LEAF CLASSIFICATION." Jurnal Ilmu Komputer dan Informasi 9, no. 2 (2016): 96. http://dx.doi.org/10.21609/jiki.v9i2.385.

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Plants play important roles for the existence of all beings in the world. High diversity of plant’s species make a manual observation of plants classifying becomes very difficult. Fractal dimension is widely known feature descriptor for shape or texture. It is utilized to determine the complexity of an object in a form of fractional dimension. On the other hand, lacunarity is a feature descriptor that able to determine the heterogeneity of a texture image. Lacunarity was not really exploited in many fields. Moreover, there are no significant research on fractal dimension and lacunarity combina
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18

Shijie, Han, Pan Jianping, and Wang Dehong. "Fractal dimension ofPopulus davidiana leaf surface rough extent." Journal of Northeast Forestry University 6, no. 1 (1995): 39–42. http://dx.doi.org/10.1007/bf02843213.

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19

BACKES, ANDRÉ RICARDO, DALCIMAR CASANOVA, and ODEMIR MARTINEZ BRUNO. "PLANT LEAF IDENTIFICATION BASED ON VOLUMETRIC FRACTAL DIMENSION." International Journal of Pattern Recognition and Artificial Intelligence 23, no. 06 (2009): 1145–60. http://dx.doi.org/10.1142/s0218001409007508.

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Texture is an important visual attribute used to describe the pixel organization in an image. As well as it being easily identified by humans, its analysis process demands a high level of sophistication and computer complexity. This paper presents a novel approach for texture analysis, based on analyzing the complexity of the surface generated from a texture, in order to describe and characterize it. The proposed method produces a texture signature which is able to efficiently characterize different texture classes. The paper also illustrates a novel method performance on an experiment using t
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20

Lai, Yongkang, Xihan Mu, Weihua Li, et al. "Correcting for the clumping effect in leaf area index calculations using one-dimensional fractal dimension." Remote Sensing of Environment 281 (November 2022): 113259. http://dx.doi.org/10.1016/j.rse.2022.113259.

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21

Du, Ji-xiang, Chuan-Min Zhai, and Qing-Ping Wang. "Recognition of plant leaf image based on fractal dimension features." Neurocomputing 116 (September 2013): 150–56. http://dx.doi.org/10.1016/j.neucom.2012.03.028.

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22

Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form." International Journal of Artificial Life Research 3, no. 3 (2012): 41–63. http://dx.doi.org/10.4018/jalr.2012070104.

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The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors
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23

Qiu, Li, Yong-Gui Li, Yan-Ping Xiong, and Xiao-Dong Chen. "Effects of humid and hot environment on fiber composites in cooling towers." Thermal Science 25, no. 2 Part B (2021): 1321–28. http://dx.doi.org/10.2298/tsci200421029q.

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Polyvinyl chloride materials used in cooling towers always lead to damage and low efficiency due to the hot and humid environment. This paper suggests a glass fiber reinforced material for a better performance. An optimal fractal distribution-of glass fibers in the composite matrix is experimentally obtained when the fractal dimensions are between 0.6 and 0.9.
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Dobrescu, Gianina, Ramona Georgescu-State, Florica Papa, Jacobus (Koos) Frederick van Staden, and Razvan Nicolae State. "Fractal Properties of Composite-Modified Carbon Paste Electrodes—A Comparison between SEM and CV Fractal Analysis." Fractal and Fractional 8, no. 4 (2024): 205. http://dx.doi.org/10.3390/fractalfract8040205.

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The fractal properties of carbon paste electrodes (CPEs) and carbon paste electrodes modified with ionic liquid (IL), AuTiO2/graphene oxide, and IL/AuTiO2/graphene oxide were investigated using scanning electron microscopy (SEM), and cyclic voltammetry (CV). The impact of fractal dimensions and self-similarity ranges on electrochemical responses was underlined. It was proved that a higher fractal dimension and a broad self-similarity domain lead to a higher electrochemical response. Results indicated that IL/AuTiO2/graphene oxide composite-modified CPEs are a great candidate to be used as elec
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25

MOHAMMADI, SHAPOUR. "EFFECT OF OUTLIERS ON THE FRACTAL DIMENSION ESTIMATION." Fractals 19, no. 02 (2011): 233–41. http://dx.doi.org/10.1142/s0218348x11005324.

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The effect of outliers on estimation of the fractal dimension of experimental chaotic and stock market stochastic data series is investigated. The results indicate that influential observations of a magnitude of mean ±5 standard deviations can lead to a distortion of fractal dimension estimations by as much as 40% for short (e.g. 500 observations) time series data. Moreover, the box dimension estimation method is more sensitive to outliers than information and correlation dimension estimation methods and the effect of outliers decreases as the number of observations increases. Application of o
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BABADAGLI, TAYFUN, and KAYHAN DEVELI. "ON THE APPLICATION OF METHODS USED TO CALCULATE THE FRACTAL DIMENSION OF FRACTURE SURFACES." Fractals 09, no. 01 (2001): 105–28. http://dx.doi.org/10.1142/s0218348x01000464.

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This paper presents an evaluation of the methods applied to calculate the fractal dimension of fracture surfaces. Variogram (applicable to 1D self-affine sets) and power spectral density analyses (applicable to 2D self-affine sets) are selected to calculate the fractal dimension of synthetic 2D data sets generated using fractional Brownian motion (fBm). Then, the calculated values are compared with the actual fractal dimensions assigned in the generation of the synthetic surfaces. The main factor considered is the size of the 2D data set (number of data points). The critical sample size that y
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27

JAIN, PS. "Fractal dimensions of clouds around Madras." MAUSAM 40, no. 2 (2022): 85–90. http://dx.doi.org/10.54302/mausam.v40i2.2133.

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Following lead from Lovejoy's (1982) investigations the structure of radar determined clouds around Madras in northeast monsoon season (October-November 1986) was investigated.
 
 Six hundred cloud echo samples having area between 50 and 5350 sq. km detected within 200 km radius by a high power S-band radar located at Madras were analysed for the relation between their perimeter and area.
 
 Consistency of the relation between the perimeter (P) and area (A) through a log P vs log A plot and of fractal dimensions (D) of cloud perimeter, has been established and conclusions d
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28

Fisher, Tony J. "Black Dots: Newton's Method and a Simple One-Dimensional Fractal." Mathematics Teacher 94, no. 9 (2001): 734–37. http://dx.doi.org/10.5951/mt.94.9.0734.

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Students in a standard calculus course learn Newton's method for finding the root of a differentiable function. Although they may often see a diagram that visually demonstrates how this method works, it often soon becomes yet another algorithm to memorize or to program into a calculator. In addition, students are sometimes told that using Newton's method on simple complex-valued functions can lead to beautiful fractal patterns. However, the connection between the sequence of steps that they have learned and the corresponding fractal images is fuzzy at best. This article describes a calculator
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29

Imashev, S. A., and M. E. Cheshev. "Estimation of fractal dimension of rock samples fracture surface." Geoinformatika, no. 1 (2021): 36–44. http://dx.doi.org/10.47148/1609-364x-2021-1-36-44.

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An approach to estimate fractal dimension of a microphotograph of rock sample fracture surface using the Differential Box Counting (DBC) method is presented. The difference between this algorithm and the classical method for fractal dimension calculation is in that the grayscale levels of pixels of analyzed image are taken into account. This approach does not require initial binarization of the image, which is poorly applicable for estimation of fractal dimension of real objects, such as microphotographs of rock sample surface, which in turn does not lead to the loss of useful information. Tes
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30

Cao, Xiaomeng, Yuan Gao, Jingwei Cui, et al. "Pore Characteristics of Lacustrine Shale Oil Reservoir in the Cretaceous Qingshankou Formation of the Songliao Basin, NE China." Energies 13, no. 8 (2020): 2027. http://dx.doi.org/10.3390/en13082027.

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Shale oil is hosted in nanopores of organic-rich shales, so pore characteristics are significant for shale oil accumulation. Here we analyzed pore characteristics of 39 lacustrine shale samples of the Late Cretaceous Qingshankou Formation (K2qn) in the Songliao Basin, which is one of the main shale oil resource basins in China, using field emission-scanning electron microscopy (FE-SEM), and low-pressure nitrogen adsorption. We accomplished fractal analysis, correlation analysis using correlation matrix and multidimensional scaling (MDS), and prediction of fractal dimensions, which is the first
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31

Kong, Bowen, Yuntian Yan, Huan He, Jing Yu, Qizhi Chen, and Baoping Zou. "Strength and Fractal Characteristics of Artificial Frozen–Thawed Sandy Soft Soil." Fractal and Fractional 8, no. 7 (2024): 393. http://dx.doi.org/10.3390/fractalfract8070393.

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In regions with sandy soft soil strata, the subway foundation commonly undergoes freeze–thaw cycles during construction. This study focuses on analyzing the microstructural and fractal characteristics of frozen–thawed sandy soft soil to improve our understanding of its strength behavior and stability. Pore size distribution curves before and after freeze–thaw cycles were examined using nuclear magnetic resonance technology. Additionally, fractal theory was applied to illustrate the soil’s fractal properties. The strength properties of frozen remolded clay under varying freezing temperatures an
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Plotze, Rodrigo de Oliveira, Maurício Falvo, Juliano Gomes Pádua, et al. "Leaf shape analysis using the multiscale Minkowski fractal dimension, a new morphometric method: a study with Passiflora (Passifloraceae)." Canadian Journal of Botany 83, no. 3 (2005): 287–301. http://dx.doi.org/10.1139/b05-002.

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A new method is proposed for the extraction of morphometric characteristics of plant leaf structures. A sample of 10 species of the genus Passiflora (P. coriacea Juss., P. foetida L., P. miersii Mast., P. organensis Gardner, P. pohlii Mast., P. suberosa L., P. amethystina J.C. Mikan, P. caerulea L., P. gibertii N.E.Br., P. maliformis L.) was used in an experiment to test the method. This genus shows a wide range of leaf forms, but there are some species pairs or groups whose morphological similarity makes their correct identification difficult. The multiscale function of the Minkowski fractal
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Wu, J. S., S. S. Krishnan, and G. M. Faeth. "Refractive Indices at Visible Wavelengths of Soot Emitted From Buoyant Turbulent Diffusion Flames." Journal of Heat Transfer 119, no. 2 (1997): 230–37. http://dx.doi.org/10.1115/1.2824213.

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Measurements of the optical properties of soot, emphasizing refractive indices, are reported for visible wavelengths (350–800 nm). The experiments considered soot in the fuel-lean (overfire) region of buoyant turbulent diffusion flames in the long residence time regime where soot properties are relatively independent of position in the overfire region and residence time. Flames fueled with acetylene, propylene, ethylene, and propane that were burning in still air provided a range of soot physical and structure properties. Measurements included soot composition, density, structure, gravimetric
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Cheng, Lei, Yan Zhen Yu, Juan Tan, and Yong Sun. "Study on Energy Consumption Distribution of High Ferric-Based Silicon Coagulant Using Fractal Dimension." Applied Mechanics and Materials 295-298 (February 2013): 1389–92. http://dx.doi.org/10.4028/www.scientific.net/amm.295-298.1389.

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High ferric-based silicon coagulant is a kind of new self-made coagulant. The high ferric content was introduced in the preparation process of the coagulant, and the effect was good in dealing with simulated industrial wastewater with lead. The beaker test indicated that the lead removal rate reached the highest 96.48% when the rapid stirring speed was 300r/min and stirring time was 1min, low stirring speed was 80r/min and stirring time was 15min, the dosage of the coagulant was 3.5ml/L. And the fractal dimension of flocs was 1.67674 under that optimum conditions. The low stirring stage was di
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YUE, Z. Y., B. ZHANG, G. WINNEWISSER, and J. STUTZKI. "ON THE DYNAMICAL EVOLUTION OF THE FRACTAL STRUCTURE OF INTERSTELLAR MEDIUM." Fractals 01, no. 04 (1993): 908–16. http://dx.doi.org/10.1142/s0218348x93000952.

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Two-dimensional compressible turbulence in a self-gravitating, magnetic interstellar medium is calculated as an initial value problem. It is shown that even if the initial density distribution is homogeneous and the initial velocity distribution contains only a few Fourier components, the nonlinear interaction among the Fourier components will generate more and more Fourier components and lead to a turbulent and fractal structure in the interstellar medium. The calculations are carried out for three different initial states. In order to see the time evolution, detailed density distributions an
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Zhang, Lan, Jing Wen, Ming Liu, and Guangzhen Xing. "A Revised Continuous Observation Length Model of Rough Contact without Adhesion." Mathematics 10, no. 20 (2022): 3764. http://dx.doi.org/10.3390/math10203764.

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The real contact area of rough surfaces has significant importance in many engineering applications, such as tribology, wear, lubrication and seals. A continuous observation length-dependent mechanic model of rough contact without adhesion is proposed, which assumes that the rough surface is divided into ideal subplanes. However, the model ignores the elastoplastic deformation of asperities, and the standard deviation of ideal subplanes’ heights is assumed to vary linearly with continuous observation length, which is not precise for all the surface fractal dimensions. In this work, a revised c
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FREDERIKSEN, RICHARD D., WERNER J. A. DAHM, and DAVID R. DOWLING. "Experimental assessment of fractal scale similarity in turbulent flows. Part 2. Higher-dimensional intersections and non-fractal inclusions." Journal of Fluid Mechanics 338 (May 10, 1997): 89–126. http://dx.doi.org/10.1017/s0022112096004077.

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Results from an earlier experimental assessment of fractal scale similarity in one-dimensional spatial and temporal intersections in turbulent flows are here extended to two- and three-dimensional spatial intersections. Over 25000 two-dimensional (2562) intersections and nearly 40 three-dimensional (2563) intersections, collectively representing more than 2.3 billion data points, were analysed using objective statistical methods to determine which intersections were as fractal as stochastically scale-similar fractal gauge sets having the same record length. Results for the geometry of Sc [Gt ]
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PIETRONERO, L. "THEORETICAL CONCEPTS FOR FRACTAL GROWTH AND SELF-ORGANIZED CRITICALITY." Fractals 03, no. 03 (1995): 405–14. http://dx.doi.org/10.1142/s0218348x95000333.

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We discuss the properties of irreversible growth models that lead to self-organized fractal structures or to scale invariant distributions. In particular we compare these models with the usual critical phenomena and point out that the irreversible dynamics represents the major conceptual difference with respect to phase transition. This situation requires the introduction of new theoretical concepts which focus on this particular feature. We discuss how the Fixed Scale Transformation method allows us to deal with these properties, to understand the self-organized nature of these systems, and t
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Maryenko, N. I., and O. Yu Stepanenko. "Fractal dimension of skeletonized MR images as a measure of cerebral hemispheres spatial complexity." Reports of Morphology 28, no. 2 (2022): 40–47. http://dx.doi.org/10.31393/morphology-journal-2022-28(2)-06.

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In recent decades, fractal analysis has been increasingly used in various scientific fields, including neuroscience; this method of mathematical analysis allows you to quantify the space filling degree of the studied object and the degree of its spatial configuration complexity. The aim of the study was to determine the values of the fractal dimension of the cerebral hemispheres using fractal analysis of skeletonized magnetic resonance brain images. The present study used magnetic resonance brain images of 100 relatively healthy individuals (who had no structural changes in the brain) of both
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40

Yu, Yanzhen, Yong Sun, Juan Tan, and Jichao Zhang. "Application of lead flocs fractal dimension by new poly-ferric-silicon coagulant." Desalination and Water Treatment 32, no. 1-3 (2011): 453–58. http://dx.doi.org/10.5004/dwt.2011.2694.

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Hui, Z., Y. Xia, Y. Nie, et al. "FRACTAL DIMENSION BASED SUPERVISED LEARNING FOR WOOD AND LEAF CLASSIFICATION FROM TERRESTRIAL LIDAR POINT CLOUDS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-1-2020 (August 3, 2020): 95–99. http://dx.doi.org/10.5194/isprs-annals-v-1-2020-95-2020.

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Abstract. Terrestrial Laser scanner has been widely used in the field of forestry. Wood-leaf separation is the fundamental step to most applications of forestry. This paper presented a robust supervised learning method for wood and leaf classification by developing four new feature vectors. Fractal dimension is first calculated to indicate the difference of regularity or roughness between wood and leaf. Zenith angle and variation are presented to distinguish trunks or branches from leaves. The adaptive axis direction of cylinder is adopted to calculate the local point density precisely. Experi
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VALDEZ-CEPEDA, RICARDO DAVID, DANIEL HERNÁNDEZ-RAMÍREZ, BLANCA MENDOZA, JOSÉ VALDÉS-GALICIA, and DOLORES MARAVILLA. "FRACTALITY OF MONTHLY EXTREME MINIMUM TEMPERATURE." Fractals 11, no. 02 (2003): 137–44. http://dx.doi.org/10.1142/s0218348x0300163x.

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Interest in climate change has increased over the last 30 years due largely to global predictions associated with the greenhouse effect, which appear to lead to a substantial increase in planetary temperature. Implications of such results have led many scientists to examine climatic records from different regions of the world in order to understand temperature behavior. However, many researchers have noted that changes in temperature variability are also important in determining the future temperature distributions. In this context, we have analyzed a long-term record of monthly extreme minimu
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Costa, Carlos, Lianne M. Dwyer, Pierre Dutilleul, et al. "Morphology and fractal dimension of root systems of maize hybrids bearing the leafy trait." Canadian Journal of Botany 81, no. 7 (2003): 706–13. http://dx.doi.org/10.1139/b03-058.

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A rapid and accurate assessment of root morphological characteristics can be important for identifying promising plant genotypes. Scanner-based image analysis has made the measurement of root morphology faster, more accurate, and less subjective, and allows for estimation of fractal dimension (FD). We used scanner-based image analysis to investigate root morphology in leafy vs. conventional maize (Zea mays) genotypes. Two experiments were conducted following a completely randomized design with ten and five replicates. In the first experiment, treatments were factorial combinations of four hybr
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Göritz, Dietmar, Horst Raab, Joachim Fröhlich, and Peter G. Maier. "Surface Structure of Carbon Black and Reinforcement." Rubber Chemistry and Technology 72, no. 5 (1999): 929–45. http://dx.doi.org/10.5254/1.3538843.

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Abstract From scanning tunneling microscopy (STM) and atomic force microscopy (AFM) measurements, it was found that the lateral dimensions of the nanocrystallites systematically decrease with decreasing diameter of the primary particles. Furthermore these experiments suggest that these nanocrystallites, unregularly tilted, form the rough surface of carbon blacks. Hence, the activity of carbon black is the result of the size of the nanocrystallites and the degree of disorder on the surface. Temperature treatments of carbon black lead to a continuous increase of the lateral dimensions of the cry
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Gao, Yuan, Hongwen Jing, and Zefu Zhou. "Fractal analysis of pore structures in graphene oxide-carbon nanotube based cementitious pastes under different ultrasonication." Nanotechnology Reviews 8, no. 1 (2019): 107–15. http://dx.doi.org/10.1515/ntrev-2019-0010.

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Abstract Nano cement additive using a hybrid of graphene oxide (GO) and multi-walled carbon nanotubes (MWCNTs) combines the excellent affinity of GO and the superior mechanical properties of MWCNTs. Ultrasonication is the key process to disperse the GO/MWCNTs and further optimizes the pore structures of cement-based pastes. Fractal dimension can effectively and quantitatively characterize the pore structures of cementitious composites. The present study investigates the fractal dimensions of pore structures of GO/MWCNT-OPC pastes under power- and time-controlled ultrasonication based on the me
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Yan, Loh Guan, Nuryazmin Ahmat Zainuri, and Mohd Zaki Nuawi. "Characterization of Musical Data Signals Resulting from Traditional Musical Instruments Using Fractal Features." Jurnal Kejuruteraan si6, no. 2 (2023): 167–78. http://dx.doi.org/10.17576/jkukm-2023-si6(2)-18.

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Musical instruments are usually distinguished by their sound produced through human perception which may lead to misinterpretation due to auditory perception bias and other disturbances. Therefore, recognition using music signals is carried out to help characterize signals from different musical instruments. Fractal analysis is a mathematical tool used to study complex and irregular patterns in various systems. In this study, fractal analysis was used to study and analyze musical notes signal data from different instruments. The fractal analysis method used is the box counting method. The trad
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Landis, Eric N. "Damage variables based on three-dimensional measurements of crack geometry." Strength, Fracture and Complexity: An International Journal 3, no. 2-4 (2005): 163–73. https://doi.org/10.3233/sfc-2005-056.

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Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this work, using three-dimensional measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties (surface area, volume, and fractal dimension) of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined f
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Li, Weihua, and Xihan Mu. "Using fractal dimension to correct clumping effect in leaf area index measurement by digital cover photography." Agricultural and Forest Meteorology 311 (December 2021): 108695. http://dx.doi.org/10.1016/j.agrformet.2021.108695.

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Suo, Yu, Fenfen Li, Qiang Liang, Liuke Huang, Liangping Yi, and Xu Dong. "Weight-Based Numerical Study of Shale Brittleness Evaluation." Symmetry 17, no. 6 (2025): 927. https://doi.org/10.3390/sym17060927.

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The implementation of lean drilling and completion design techniques is a pivotal strategy for the petroleum and natural gas industry to achieve green, low-carbon, and intelligent transformation and innovation. These techniques significantly enhance oil and gas recovery rates. In shale gas development, the shale brittleness index plays a crucial role in evaluating fracturing ability during hydraulic fracturing. Indoor experiments on Gulong shale oil were conducted under a confining pressure of 30 MPa. Based on Rickman’s brittleness evaluation method, this study performed numerical simulations
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Yu, Xianzheng, Hua Liu, Xiaolin Fan, Liangyu Zhu, Chengqi Zhang, and Shiyi Zhang. "Research on the Permeability and Pore Structure Distribution Characteristics of High-Performance Mortar for Surface Treatment of Bridge Piers and Columns." Buildings 14, no. 3 (2024): 811. http://dx.doi.org/10.3390/buildings14030811.

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In marine environments, bridge piers and columns are prone to corrosion caused by harmful media, particularly chloride ions. This corrosion can lead to cracking of the steel bars in the protective layer of the bridge piers. To enhance the corrosion resistance of concrete in bridge piers, this article introduces the use of nanoclay-modified cement mortar. This innovative material offers high-performance surface treatment options that can effectively slow down the erosion process of harmful media and reduce the risk of bridge pier column cracking. To evaluate the ion erosion resistance of this n
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