Fractal Dimension Values Research Articles

A Fractal Dimension Analysis to Evaluate the Change in the Alveolar Osseous Structure of Mandibular Incisors after Orthodontic Treatment: A Retrospective Study

Introduction: As bone traces tooth movement during orthodontic treatment, leading to biological response of the surrounding tissues of the teeth resulting in remodelling of the socket, favourable bone response is expected after incisor retraction. Orthodontic treatment causing changes in alveolar bone can be evaluated using Fractal dimension (FD) analysis, a mathematical method of information processing, where the input data is in the form of an image and generated information is displayed as numbers. Aim: To evaluate changes in the trabecular structure of alveolar bone after incisor retraction in the mandibular symphysis region in adult patients using fractal analysis. Materials and Methods: This retrospective study was conducted with digital Orthopantomogram (OPG) of 30 patients with class I and class II malocclusion with mandibular incisor protrusion treated with extraction and retraction of anterior teeth were taken with standard protocols at the three different periods, before orthodontic treatment (T0), before retraction (T1) and after retraction of anterior teeth (T2) included in the study. Regions of interest were located between the apices of mandibular incisors. FD was calculated using ImageJ software. Statistical Analysis was carried out by repeated Analysis of Variance (ANOVA) test and post-hoc test. Results: Total of 30 cases were selected, out of which 15 were males and 15 females with the mean age of 21±2 years. FD values of the alveolar bone of mandibular incisors at T0 were 1.470±0.09 which reduced to 1.390±0.09 at T1 and to 1.350±0.08 at T2. This overall changes in FD values were significant (p-value=0.001). Conclusion: Fractal dimension analysis demonstrate significant changes in bone trabeculation of the mandibular symphysis region before and after orthodontic treatment. It has valuable impact in the cases of fenestration, dehiscence’s, and osteoporosis.

Fractal Dimension Analysis of Pixel Dynamic Contrast Enhanced-Magnetic Resonance Imaging Pharmacokinetic Parameters for Discrimination of Benign and Malignant Breast Lesions

Breast cancer is the most frequent cancer in women worldwide. However, its diagnosis mostly depends on visual examination of radiologic images, leading to an overdiagnosis with substantial costs. Therefore, a quantitative approach such as dynamic contrast enhanced (DCE)-magnetic resonance imaging (MRI) through pharmacokinetic (PK) modeling is required for reliable analysis. As PK parameters lack information on parameter heterogeneity, texture-based analysis is required to quantify PK parameter heterogeneity. Therefore, this study focused on determining the usefulness of fractal dimension (FD) as a potential imaging biomarker of tumor heterogeneity for discriminating benign and malignant breast lesions. Parametric maps for PK parameters, extravasation rate of contrast agent from blood plasma to extravascular extracellular space (Ktrans) and volume fraction of extravascular extracellular space (ve), were generated for the regions of interest (ROIs) under the standard model using 18 lesions. Then, tumor ROI and pixel DCE-MRI time-course data were analyzed to extract pixel values of Ktrans and ve. For each ROI, FD values of Ktrans and ve were computed using the blanket method. The FD values of Ktrans for benign and malignant lesions varied from 2.96 to 3.49 and from 2.37 to 3.16, respectively, whereas FD values of ve for benign and malignant lesions varied from 3.01 to 5.15 and 2.42 to 3.44, respectively. There were significant differences in FD values derived from Ktrans parametric maps (P = .0053) and ve parametric maps (P = .0271) between benign and malignant lesions according to the statistical analysis. Incorporating texture heterogeneity changes in breast lesions captured by FD with quantitative DCE-MRI parameters generated under the standard model is a potential marker for prediction of malignant lesions.

Fractal dimension, lacunarity, and cortical thickness in the mandible: Analyzing differences between healthy men and women with cone-beam computed tomography.

The objective of this study was to assess the fractal dimension, lacunarity, trabecular microarchitecture parameters, and cortical linear measurements in the mandibles of male and female individuals to identify differences between them. In total, 116 cone-beam computed tomography scans of healthy individuals of different ages (57 men and 59 women, aged between 20 and 60 years) were selected. The following bone parameters were measured: 1) buccal, lingual, and basal cortical bone thickness in 5 standard parasagittal sections (the midline, the left and right sides of the lower lateral incisors, and the left and right sides of the lower canines); 2) the bone volume fraction of 10 sequential axial sections from each patient by creating a volume of interest in the area between the lower canines; and 3) fractal dimension and lacunarity using grayscale images of the same region of the volume of interest in the anterior mandible. Spearman correlation coefficients and the Mann-Whitney test were used. A significant and positive correlation was found between age and cortical thickness, especially in the region of the central incisors. Significant differences between sexes in terms of fractal dimension, lacunarity, and bone volume were found. Women revealed lower fractal dimension values and higher lacunarity and bone volume ratio values than men. Fractal dimension, lacunarity, trabecular bone volume, and cortical thickness were different between men and women of different ages.

Analysis of non-equilibrium 4D dynamical system with fractal fractional Mittag–Leffler kernel

In this article, we presents the theoretical and numerical study of the four dimensional chaotic system which has no equilibrium point in the sense of fractal-fractional Mittag–Leffler kernel. By using the approach of fixed point theory, the existence and uniqueness of solution for the considered model is studied. The approximate solution is acquired by applying the technique of fractional Newton’s polynomial interpolation. The numerical simulations of the approximate results are presented for different fractal dimension and fractional orders. From the figures we obtained the butterfly-type attractor by using different values of fractal dimension which shows symmetric form. Furthermore, fractal and fractional operators show significant impacts on the dynamics of the non-linear chaotic systems.

Structural and Fractal Analysis of Soil Cracks Due to the Roots of Setaria Viridis

Soil surfaces form complex crack networks as a result of water loss and shrinkage. A crack network destroys the integrity of the soil and becomes the main factor affecting rainfall infiltration, slope instability and soil integrity. In this paper, a soil fracture network is quantified using fractal characteristics and fractal dimensions, and the soil fracture network is identified and calculated using digital image processing technology. The fracture network of silty clay with different setaria viridis root content is studied during the process of evaporation. Saturated mud is prepared by taking soil samples and collecting setaria viridis roots. The content of setaria viridis roots in each saturated mud sample is 0 g, 0.1 g, 0.2 g and 0.3 g. In the artificial climate environment simulation system, thin-layer root soil is dried by controlling the temperature and humidity to simulate dry climate conditions. During the test, the crack development process is recorded using a digital camera. The results show that when the root content is 0, 0.1 g, 0.2 g and 0.3 g, the water content values when a fissure is generated are 35.2%, 41.2%, 42% and 46.4%, and the initial fractal dimension values are 1.100, 1.106, 1.112 and 1.115, respectively. The fractal dimension value increases rapidly in the early stage of fissure generation, and it reaches the maximum value when the water content reaches 13.66%, 15.2%, 15.66% and 17.98%, respectively. According to the change law of the fractal dimension, the fractal dimension increases rapidly following the initial appearance of the fracture, and, with a continuous reduction in water content in the later stage, the fracture characteristics gradually stabilize, and the change rate of the fractal dimension becomes slow.

Structural insights into mechanisms of rapid harvesting of microalgae with pH regulation by magnetic chitosan composites: A study based on E-DLVO model and component fluorescence analysis

Magnetic harvesting of microalgae depends on the interface interactions between microalgal cells and flocculants, and thus it is important to find a reasonable evaluation method understand these interface interactions. In this effort, we discussed the formation mechanism and pH regulation of microalgae magnetic harvesting via magnetic chitosan (Fe3O4@SiO2-CS) synthesized by a micro-emulsion method. The flocculation performances and mechanisms during the harvesting of microalgae by the novel flocculant were evaluated. The synthesis process and structure were determined by XRD, FT-IR, SEM and XPS, and the results indicated that Fe3O4@SiO2-CS was successfully prepared. The collection efficiency of 96.52 % was achieved for Chlorella vulgaris within 3 min using Fe3O4@SiO2-CS with the Fe3O4@SiO2 and CS mass ratio of 1:3 under pH 1.0. Moreover, this study introduced the two-dimension fractal dimension and extended Derjaguin-Landau-Verwey-Overbeek (E-DLVO) model to evaluate the harvesting performances and mechanisms of Fe3O4@SiO2-CS. Experimental results showed that a strong electrostatic interaction was formed under acidic conditions between Fe3O4@SiO2-CS and microalgae cells with D2 = 1.82 (fractal dimension value). The hydrophobic tryptophan-like amino acid was observed in the slime-extracellular polymeric substances (S-EPS) secreted by microalgae. S-EPS was found to be a significant substance to promote harvesting performance when the system was neutral or alkaline. This work provides deeper insights into microalgae harvesting by Fe3O4@SiO2-CS as well as reasonable mechanisms to illustrate the interaction of Fe3O4@SiO2-CS and microalgae under different pH values.

The Role of Fractal Micro-Pore to Absorption of Methane Gas, Case Study: Coal of Tanjung Formation, Arang Alus Area, Banjar District, South Kalimantan, Indonesia

The Tanjung Formation is one of the coal bearing formations in the Barito Basin, South Kalimantan. The coal seams in the Tanjung Formation in the Arang Alus area have 4 (four) seams,there are seam A, B, C, and D. The age of these coal seams are Eocene - Oligocene with a thickness between 0.5 - 2 meters. This study aims to determine the characteristics of micropore fractal and methane gas absorption from coal samples taken by channel sampling on exposed coal in the open pit. The method used is SEM analysis, vitrinite reflectance (Ro,max), adsorption isotherm, and fractal calculation. The four coal seams based on vitrinite reflectance values (0.52 %- 0.62 belong to the sub-bituminous rank. Based on the methane gas absorption capacity for coal seam C of 450 SCF/ton while coal seams A, B and D of 308 SCF/ton, 336 SCF/ton and 407 SCF/ton, the fractal pore dimension value in seam coal C = 1.963 is higher than seam coal A = 1.933, B = 1.940 , and D = 1.943. The small size of the fractal pore dimension value caused by the degree of regularity of the micropore distribution in each coal seam methane differences.

Mutations along human chromosomes: How randomly scattered are they?

The diversity of mutations in human chromosomes is nowadays very well documented. The mutations characterize populations in the world as well as genetic causes of diseases. In the approach that we follow, we study the patterns of gaps between mutations by means of the rescaled range analysis and the fractal dimension estimates. The results for chromosomes 1 to 22 and X indicate the existence of the so-called Hurst phenomenon in all of them. The interpretation of this outcome entails the presence of long-range correlations and we propose an explanation based on the genomic feature dubbed linkage disequilibrium, a nonrandom association of alleles at different loci. An unexpected outcome is the noteworthy uniform reduction in the Hurst phenomenon when considering the centimorgan metric instead of base position units. By contrast, such uniform reduction is not observed with the fractal dimension values.

Fractal analysis of dental periapical radiographs: A revised image processing method

To assess trabecular bone structure as calculated with fractal analysis by 2 binarization processes: White and Rudolph's original method (WR.o) and a revised version (WR.r). Fractal dimension (FD) values calculated with WR.r (FD.r) and a gray-scale-based method (FD.f) were also compared. FD, histogram parameters, and lacunarity were compared by dentate status, jaw location, and sex. Regions of interest from digital periapical radiographs were defined below the teeth roots and in the edentulous sites of 37 patients. Histograms were assessed for pixel values. Binarization was performed with WR.o and then with WR.r, in which the outliers were removed. FD was assessed using WR.r (FD.r) and (FD.f). Histograms were assessed to obtain pixel values. Lacunarity was calculated. WR.r revealed fewer trabeculae, branches, and junctions than WR.o (P < .0001). The majority of the mean differences between FD.r and FD.f were within the 95% CI. Dentate areas had greater mean gray levels than partially edentulous areas (P=.0027). FD.f was higher in the mandible (P=.01), but gray-level SD (P < .0001) and lacunarity (P=.02) were greater in the maxilla. FD.f and lacunarity were higher (P=.0005) and lower (P=.0014) in males, respectively. WR.r was effective in revealing skeletonized bone trabeculae by removing non-trabecular noise. FD.r and FD.f revealed good agreement. FD.f, histogram parameters, and lacunarity differed based on dentate status, jaw location, and sex.

Does childhood chemotherapy affect mandibular bone structures in a lifetime?

Chemotherapy, one of the most important treatment modalities for treating childhood cancers, is a major cause of bone loss in patients and survivors. This study aimed to evaluate mandibular bone structures in childhood cancer survivors (CCSs) by means of fractal dimension (FD) analysis and the Klemetti index (KI), and to compare them with regard to the control group. In this retrospective study, the panoramic radiographs of 49 CCSs were included as the study group and the panoramic radiographs of 49 cancer-free volunteers were included as the control group. Based on the panoramic radiographs, FD and KI were determined. No significant differences were observed between the study and control groups in terms of mean FD values for regions of interest (ROIs) ROI_1, ROI_2 and ROI_3 (p = 0.750, p = 0.490 and p = 0.910, respectively). The mean FD values for ROI_1 for the study and control groups were 1.08 ±0.18 and 1.07 ±0.14, respectively. The mean FD values for ROI_2 for the study and control groups were 1.11 ±0.13 and 1.09 ±0.13, respectively. The mean FD values for ROI_3 for the study and control groups were 1.15 ±0.14 and 1.15 ±0.15, respectively. Statistically significant differences between the study and control groups were noted only in the distribution of the KI categories (p = 0.015). Childhood chemotherapy may affect mandibular bone structures during a lifetime. The Klemetti index should be considered a useful clinical diagnostic tool for the examination of mandibular bone structures.

Relationship between fracture toughness and fractal dimensional increment in two types of dental glass-ceramics with different fracture surface roughness.

Previous studies have reported the fractal dimensional increment of glass-ceramic fracture surfaces. The objective of this study was to determine the relationship between fracture toughness and fractal dimensional increment of two dental glass-ceramics with different volume fraction of crystals and different fracture surface roughness. Bar-shaped specimens were prepared from lithium disilicate (LDS) and nanofluorapatite (NFA) glass-ceramics. One face of each specimen was indented using a Knoop diamond at 25N (LDS) or 10N (NFA) followed by loading in 4-point, or 3-point flexure, respectively, until failure. Fracture toughness (Kc) was calculated using the surface crack in flexure (SCF) technique (ASTM C1421). Epoxy replicas of the fracture surfaces were scanned using the atomic force microscope (AFM) followed by noise filtering. The FRACTALS software was used to determine the fractal dimensional increment (D*) by the Minkowski cover algorithm. Median (25%, 75% quartiles) fracture toughness of LDS bars were 1.62 (1.59, 1.69)MPam1/2 and NFA bars were 0.68 (0.66, 0.74)MPam1/2, respectively. The median fractal dimension (D) value (25%, 75% quartiles) before noise filtering were 2.16 (2.15, 2.17) and after noise filtering were 2.14 (2.14, 2.15) for LDS and before noise filtering were 2.29 (2.21, 2.38) and after noise filtering were 2.17 (2.17, 2.18) for NFA. Median (25%, 75% quartiles) surface roughness (Ra) before noise filtering were 139 (119, 188)nm and after noise filtering were 137 (118, 187)nm for LDS and before noise filtering were 7 (6, 15)nm and after noise filtering were 7 (6, 15)nm for NFA. Noise filtering successfully eliminated noise from the material with smooth fracture surfaces (NFA), decreasing the measured fractal dimension. The NFA data fit a Kc vs. D*1/2 statistical model for fused silica previously tested using a similar technique. The equation relating fracture toughness to the fractal dimension was modified, accounting for the toughening mechanisms. Fractal analysis with noise filtering can be used to estimate the fracture toughness of dental glass-ceramics that do not exhibit crack bridging.

Estimating termite population size using spatial statistics for termite tunnel patterns

Subterranean termites build underground tunnels for foraging. The obtained food is transported to the nest through these tunnels, and consumed to maintain the termite colony. In this process, termites can cause damage to wooden structures. To develop effective control strategies to reduce termite damage, it is important to know the sizes of the termite populations in the tunnels. In this study, we proposed a method for estimating the termite population size using the spatial statistic indices including fractal dimension (FD), local density (LD), and join count statistic (JCS) for the tunnel patterns. However, the method needs further improvement to be applied in field conditions. For the method, we generated 8,000 tunnel pattern images (1,000 images for each N) using an agent-based model based on experimental data. Here, N (= 3, 4, ..., 10) represents the number of termites participating in tunnel construction in the simulation. Subsequently, we calculated the FD, LD and JCS values of the tunnel pattern and trained and verified the k-nearest neighbors (KNN) algorithm, using 5,600 and 2,400 images, respectively. The population size (N) was estimated based on the FD, LD and JCS using the KNN algorithm. The estimated accuracy for all N was 60% to 97% in the range of k = 1 to 300. If the model for tunnel pattern generation includes heterogeneous environmental conditions, the proposed method could be used to effectively estimate the actual number of termite populations. Finally, we briefly discuss the challenges affecting our model, and how these could be overcome.

Characterization of Mechanical Material Properties with Fractal Analysis

Material selection is one of the main factors in the building structure. In this study, an alternative method was implemented using fractal analysis method. The use of this method can be used for cost savings and accident rates to identify the mechanical properties of each material. The purpose of this research is to study the time series resulting from experiments using piezo film sensors using fractal analysis and investigating the properties of different mechanical materials (poisson ratios) with different impact forces using fractal dimensions. There are four types of selected materials namely brass, copper, mild steel and stainless steel which is in round in shape. Different impact forces are generated by using an impact hammer and subsequently a vibration signal is obtained from a piezo film sensor. Using Matlab software, analysis using the fractal method was performed. The fractal dimension was obtained from the gradient values of the log-log plot and the fractal dimension was calculated for each impact force applied to each specimen. Then, fractal dimension values were compared using CES Edupack2012 for characterization of the properties of each material. It can be concluded that the value of fractal dimension increases when the impact forces increase too whereas a decrease in the poisson ratio occurs when the fractal dimensions of each material increase.

Macro-meso shear properties of alluvial-diluvial soil-rock mixture (ADSRM) subgrade fillers based on field investigation and N-method

Alluvial-diluvial deposit (ADSRM) is a special soil-rock mixture, which is composed of gravels, boulders, pebbles, and fine-grained soils carried by rivers or temporary floods. Its mechanical properties are quite different from regular soils and rocks. Based on the investigation results of alluvial-diluvial deposits in Luonan, Shaanxi Province, China, and the theory of the N-method, the shear mechanical properties of ADSRM samples with different N-values were analyzed using large-scale direct shear tests and image processing technology (IPP). Investigation results show that alluvial-diluvial deposits in the Luonan area are widely distributed, and most of complex origins and structures. The fractal dimension values of ADSRM samples only have one scale range of particle size and decrease with the increasing n value. The equivalent cohesion, internal friction angle, shear strength, and dilation value of the ADSRM sample with n = 0.55 are higher than those of other samples. The proportion of pore area, pore abundance, total crushing area, the fractal dimension of rock block contour, and equivalent diameter and abundance of rock blocks were used to characterize the pores and rock block morphology on the shear plane. The shape of most pores on the shear plane is oblate, secondly near-equiaxed, and the least long-strip. The crushing area of rock blocks on the shear plane of n = 0.55 sample is the highest, and the shape of most rock blocks is oblate and tends to develop to near-equiaxed. In summary, the macro-meso shear properties and engineering characteristics of the n = 0.55 sample are better than those of other samples designed by the N-method.

Insight into the mechanism of fracture properties modulated by microstructure in the myofibrillar protein and polysaccharide gel systems

The objective of this study was to investigate the mechanism of fracture properties modulated by microstructure in the myofibrillar protein (MP) and polysaccharides gel systems. Compare to the modified starch, the dietary fiber significantly improved the fracture stress and reduced the fracture strain at same concentration. The treatment with 2% dietary fiber had the highest value of fracture stress and the lowest value of fracture strain, which were 259 g and 1.12 respectively. From the skeleton structure, the Raman spectroscopy result showed that dietary fiber addition significantly reduced the intensity at 2945 cm−1, which suggested that the aggregation of hydrophobic groups was improved. The SEM showed that the treatment with 2% dietary fiber had the highest fractal dimension value of 1.7772 and the lowest lacunary value of 0.258. From the filling structure, the paraffin section showed that the polysaccharides were just simply trapped in MP gel networks and formed numerous large volumes and no-elastic of cavities. The principal component analysis suggested that the compactness of three-dimensional gel networks determined fracture stress of composite gel. The no- no-elastic of cavities formed by modified starch and dietary fiber resulted in the reduction of fracture strain. These results would promote the development of innovative nutritional meat product formulation with satisfied textural property.Graphical

Macular Vascular Complexity Analysis of Diabetes Mellitus by Swept-Source Optical Coherence Tomographic Angiography

Purpose: This study was designed to evaluate the associations between retinal vascular complexity features, including fractal dimension (FD) and blood vessel tortuosity (BVT), and the severity of diabetic retinopathy (DR) by using optical coherence tomographic angiography (OCTA). Methods: In this prospective cross-sectional study, 1,282 ocular-treatment-naive patients with type 2 diabetes mellitus (DM) (1,059 without DR and 223 with DR) registered in the community of Guangzhou, China, were enrolled. OCTA was used to measure FD and BVT in the superficial capillary plexus (SCP) and the deep capillary plexus (DCP). Univariate and multivariate linear regression analyses were performed to analyze the correlation of FD and BVT in different layers with DR severity. Results: In this study, 1,282 patients with DM (1,282 eyes), with a mean age of 64.2 ± 7.8 years, were included. FD in the DCP decreased and BVT in the DCP increased in patients with DR compared with those in patients without DR, even after adjusting for confounding factors (p < 0.05). Trend analysis showed a significant decrease in the FD values as the DR progressed, whereas the BVT progressively increased with worsening DR severity (p < 0.01). The FD in DCP had a statistically significant positive correlation with FD in SCP and a negative correlation with BVT in SCP and BVT in DCP in all of the participants, including the non-DR group, moderate DR group, and severe DR group (p < 0.01). Conclusions: FD and BVT determined using OCTA might be useful parameters for objectively distinguishing DR from non-DR and indicating DR progression.

Evolution of Morphology, Fractal Dimensions, and Structure of (Titanium) Aluminosilicate Gel during Synthesis of Zeolites Y and Ti-Y

Zeolite Y and Ti-containing zeolite Y (1%, 2% and 5% TiO2) were synthesized by a hydrothermal seed-assisted method. In order to evidence the evolution of morphology, structure, and fractal dimensions during the zeolitization process at certain time intervals, a small volume from the reaction medium was isolated and frozen by lyophilization. The obtained samples were characterized by scanning electron microscopy (SEM), wide-angle X-ray diffraction (XRD), and small-angle X-ray scattering (SAXS). The fractal dimension values of the isolated samples, calculated from SAXS data, evidenced a transition from small particles with a smooth surface (2.021) to compact structures represented by zeolite crystallites with rough surfaces (2.498) and specific organization for zeolite Y. The formation of new structures during hydrothermal treatment, the increase in crystallite size and roughness due to the continuous growth were suggested by variation of fractal dimensions values, SEM microscopy images and X-ray diffractograms. The incorporation of titanium in low concentration into the zeolite Y framework led to the obtaining of low fractal dimensions of 2.034–2.275 (smooth surfaces and compact structures). On the other hand, higher titanium concentration (2%) led to an increase in fractal dimensions indicating structures with rougher surfaces and well-defined self-similarity properties. A mechanism for zeolite synthesis was proposed by correlation of the results obtained through morphological, structural, and fractal analysis.

Can urban green space water planes be quantified? A new way of thinking about landscape planning and design

Water bodies in urban green spaces are important parts of urban landscapes, and their planar shapes are an important factor governing the creation of waterfront landscapes. To improve the aesthetics and functionality of water bodies, this paper takes Nanjing as an example for analysis to investigate whether it is possible to scientifically quantify the planar shape of urban green space water bodies. First, water bodies meeting the conditions within the municipal area were selected as the study objects for classification. Second, in view of the lack of theoretical and innovative problems in previous studies, the use of fractal theory was proposed to improve the scientificity. Finally, remote sensing data images were used to extract water body planes, and the fractal dimensions were calculated and quantitatively evaluated by coupling the box dimension method with fractal theory. The results show that the fractal dimension could be used as a quantitative parameter to determine the planar morphology of water bodies in urban green spaces, and the fractal dimension value is positively correlated with the complexity of the water body, which can be used for both quantitative assessment of the landscape aesthetics of existing water bodies in urban green spaces and theoretical support for the future design of water planar morphology.

Fractal analysis of seahorses in Mindanao, Philippines: A tale of their own

Abstract. Tabugo SR, Claver PSS. 2022. Fractal analysis of seahorses in Mindanao, Philippines: A tale of their own. Biodiversitas 23: 5233-5238. Monitoring populations of species is essential for science-driven policymaking. However, monitoring can be a daunting task for threatened and vulnerable species like seahorses. They are often threatened by overfishing and habitat destruction in the marine environment. Since they are considered a flagship species, monitoring populations in Panguil and Murcielagos Bay, which served as the home of the two common seahorses in Mindanao, Philippines, is vital. Fractals naturally occur in nature and hence can be used as possible predictors. Morphometric complexity patterns were investigated in the Hippocampus kuda and Hippocampus comes via fractal geometry to delineate irregular non-euclidean objects. The difference between fractal dimension and lacunarity values was tested between species. The hypothesis states that high fractal dimensions are deviations from the equilibrium state/chaos and, thereby, can be linked to vulnerability. High mean fractal dimension (Da) based on box-counting and coefficient of variation (CV) of the lacunarity method were found in H. kuda (F) and H. comes (F). The observed variations can be attributed to morphological complexity as they have adapted to varied microhabitats. Herewith, fractals can be a fast, easy, convenient, and non-invasive way of monitoring species. The results of the study can support conservation protection measures for the two species.

Fractal analysis of seahorses in Mindanao, Philippines: A tale of their own

Abstract. Tabugo SR, Claver PSS. 2022. Fractal analysis of seahorses in Mindanao, Philippines: A tale of their own. Biodiversitas 23: 5233-5238. Monitoring populations of species is essential for science-driven policymaking. However, monitoring can be a daunting task for threatened and vulnerable species like seahorses. They are often threatened by overfishing and habitat destruction in the marine environment. Since they are considered a flagship species, monitoring populations in Panguil and Murcielagos Bay, which served as the home of the two common seahorses in Mindanao, Philippines, is vital. Fractals naturally occur in nature and hence can be used as possible predictors. Morphometric complexity patterns were investigated in the Hippocampus kuda and Hippocampus comes via fractal geometry to delineate irregular non-euclidean objects. The difference between fractal dimension and lacunarity values was tested between species. The hypothesis states that high fractal dimensions are deviations from the equilibrium state/chaos and, thereby, can be linked to vulnerability. High mean fractal dimension (Da) based on box-counting and coefficient of variation (CV) of the lacunarity method were found in H. kuda (F) and H. comes (F). The observed variations can be attributed to morphological complexity as they have adapted to varied microhabitats. Herewith, fractals can be a fast, easy, convenient, and non-invasive way of monitoring species. The results of the study can support conservation protection measures for the two species.