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The study aims to analyse the fractal geometry of eight (eight) traditional housing facade planes, which were preserved facade originality and damaged (it is determined regarding window dimensions) in the historic urban centre of Afyonkarahisar. The scope of the study is the concept of fractal in the conceptual framework, fractal geometry and fiction, architectural and fractal fiction, explanation of the traditional Turkish housing definition and formation, determination of building tags in field survey, the box-counting method based on fractal fiction, evaluation of data and findings. The examples in this study have been selected from three-floor, pinnacle, and entrance facades in traditional housing within the "Urban Archeological Site" of the Afyonkarahisar. According to the traditional housing facades defined, the window space remained in its original state, and two different groups were identified, which was damaged originality. Two-dimensional front views of the eight samples in the two groups were drawn vectorially by taking the facade relievo. The fractal fiction between each other was analysed using the "box-counting method". The analysis of traditional housing facades preserved originality or which was damaged; originality was made according to the data obtained. [ABSTRACT FROM AUTHOR]

Purpose: Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Materials and Methods: Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. Results: All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. Conclusion: These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery. [ABSTRACT FROM AUTHOR]

We examined the behavior of different fractal dimensions when applied to study features of earthquake spatial distribution on different types of data. We first examined simulated spatial fields of points of different clustering level, following the so called Soneira-Peebles model. The model was chosen because it displays some similarity to the real clustering structure of earthquakes occurring on hierarchically ordered faults. The analysis of the capacity, clustering and correlation dimensions revealed that their behavior did not completely correlate with the clustering level of the simulated data sets. We also studied temporal variations of the fractal coefficients, characterizing the spatial distribution of the 1999 İzmit-Düzce aftershock sequence. The calculated coefficient values demonstrated analogous behavior like for the simulated data. They exposed different variability in time, but for all of them a systematic fluctuation was observed before the occurrence of the Düzce earthquake. Our analysis revealed that although fractal coefficients could be applied to measure earthquake clustering, they should be used with caution, trying to figure out the best coefficient for a certain data set. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new, simple, computationally efficient and practical method to accurately calculate effective fracture network permeabilities (EFNPs) for fracture dominated reservoirs. A set of fracture patterns from the outcrops of geothermal reservoirs in southwestern Turkey were chosen and their EFNP values were predicted using the new method; the computed permeabilities are comparable to those obtained with a commercial software package. The proposed method is based on 2-D fracture outcrop data, and is therefore limited to 2-D fracture networks. [Copyright &y& Elsevier]

There are mainly two concepts that appear with the development process of urban settlements. One of them is change and the other is sustainability or continuity. Unchanged and changed properties are strictly related to the development process itself and they differ in planned and self-generated systems. The present paper is intended to contribute to understanding the principles, which lead to the spatial evolution of cities through time. Beyazit square covering a 1km × 1km area, with its surroundings was selected for this study as it is one of the historical cores of Istanbul and has a unique character with its built environment and rich urban activities. Analyzing the changes in spatial structure in time shows the effects of the natural environment and the formerly built up environment as an initial condition. Although the general structure, which is shaped mainly by the dominance of historical environment, is unchanged, in the adaptation process for the changing social, economic and several other factors, many changes have occurred. This complicated process is examined by using the methods defined by chaos theory such as analyzing the changes in fractal dimensions in different time periods to explain the changing complexity level of spatial structure. The two key features of fractal dimension concept are generator and initiator. These features can be translated into urban pattern concept as the generation process or transformation rules and existing environment as an initial condition. Planning and selforganization represent two different processes leading to the transformation of the urban pattern. First of them is a topdown process, which has an ability to make changes on the whole urban pattern in a short time period, while second one reflects a bottomup process, where changes are made by individual decisions and they take longer to change the spatial pattern. Moreover, these two processes generally occur in different scales: Selforganization is closely related to buildings and plots while planning is generally more comprehensive and affects building blocks, transportation routes and the whole urban pattern. Because of these, the urban pattern can be classified into three main components: buildings, building blocks and roads. Fractal dimension in different time periods for each element is calculated separately. Although urban pattern is a fractal object, there is a big difference between computer generated theoretical fractals and urban pattern: Generally theoretical fractals are purely selfsimilar which is not applicable for real urban patterns. Added to this, urban pattern is a highly complex structure, the fractal dimension changes in different scales and different sub regions. Fractal generation in computer environment starts with the simple initiator object and generation rule, however, in urban realm, generally, the existing patterns are very heterogeneous and there are many interacted factors that affect the evolution process as a generation rule which result in various fractal dimensions. This feature is called as "multifractality". There are several methods to calculate fractal dimension such as: Hausdorff dimension, Self similarity dimension, Box counting dimension, Divider or ruler dimension, Lyapunov dimension, Information dimension, Dilation dimension. Box counting method is the most preferred to other methods in physical science. Box counting method is relatively easy to calculate and suitable to measure spatial elements of urban pattern. Because of these advantages, box counting method was selected to calculate the fractal dimension of uban pattern. The preliminary measurement results show that the fractal dimension of the Beyazit sample is over 1.7 that is higher than the values of 1.41.6 measured in modern settlement patterns. These results are considered to be a reflection of the complexity of the spatial structure of the study area. Detailed measurements of urban pattern revealed the multifractality of Beyazit sample. Beyazit has different fractal dimensions in different scales. The more diversity of spatial elements and heterogeneous structure of urban pattern bring together the increase in the range of fractal dimension values. On the other hand, fractal dimension values are generally over 1,7 and very close to each other with the exception of the year of 1819, which demonstrates very different pattern. Similar fractal dimensions of different time periods reflect the continuity of spatial character especially after 1900s. On the other hand, the changes in fractal dimension values are the result of spatial changes such as widened roads or changing building blocks and buildings demonstrating the relationship between fractal dimension and spatial configuration. [ABSTRACT FROM AUTHOR]

Since the late 1970s, Complexity Scientists have shown that many natural systems possess similar geometric patterns that are repeated over multiple scales of observation. This observation lead to the development of fractal geometry, as a means for determining, over progressive scales, the characteristic visual complexity of natural systems and forms. More recently it has been demonstrated that fractal geometry can also be useful for measuring the visual complexity of the constructed environment. As a result of this, it became possible, in the late 1990s to compare the fractal dimensions of both natural and constructed forms and thereby investigate the extent to which buildings are a reflection of their natural setting. The most famous examples of this provided evidence that a formal connection could be traced between the city of Amasya in Turkey and the landforms of its natural setting, and a similar argument has been made about Sea Ranch in California. With only minimal evidence, a range of conclusions were drawn from this early work about the connection and influence of a local ecology on local architecture. The present article re-tests these previous results using a more refined, computational version of the fractal analysis method. [ABSTRACT FROM AUTHOR]

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Aims: The aim of this study was to evaluate the mandibular bone changes on panoramic radiographs of thalassemia and sickle cell anemia (SCA) patients using fractal dimension (FD) analysis and to compare the findings obtained from healthy individuals., Materials and Methods: A total of 90 panoramic radiographs (from 30 patients with thalassemia, 30 patients with SCA and 30 healthy individuals) were assessed to measure FD, mandibular cortical width (MCW), panoramic mandibular index (PMI) in the mandible. Three region of interests (ROI) of angulus, corpus, and interdental bone were created. FD was calculated using ImageJ program., Results: In thalassemia group, the mean value of FD was 1.11, 1.03, and 1.02 in interdental bone, corpus, and angulus, respectively. In SCA group, the mean value of FD was 1.10, 1.05, and 1 in interdental bone, corpus, and angulus, respectively. In control group, the mean value of FD was 1.09, 1.04, and 1 in interdental bone, corpus, and angulus, respectively. FD value of interdental bone are significantly higher in thalassemia group than control group. FD values of corpus and angulus values did not show a significant difference between the groups., Conclusions: Fractal analysis may be used and recommended for evaluation of the bone changes induced by hemoglobinopathies., Competing Interests: None

Fractals are recently integrated into mathematics curriculums in Turkey. Because the integration process is successful, it is important that the studies of teaching fractals in the mathematics curriculum and textbooks should be assessed. The purpose of this study was to assess the grade 8 elementary school mathematics curriculum, textbooks and workbooks within the scope of fractal geometry. In this respect, in the first part of the study the basic characteristics of fractals were defined. And the other parts of the study, the studies in the mathematics curriculum and textbooks within the scope of fractals were evaluated and some suggestions were recommended. [ABSTRACT FROM AUTHOR]

The full diagnostic potential of the fractal complexity measure, α, of detrended fluctuation analysis (DFA) has not been realized yet. To reveal the impaired mechanisms in the blood flow regulation in patients with essential hypertension (EHT), we studied the laser Doppler flowmetry (LDF) time series by applying DFA. Forearm microvascular blood flow was measured by LDF during supine rest. After a 15 min baseline recording, microvascular response to thermal hyperemia was measured over 30 min. We found three distinct scaling regions; corresponding to the integration of local mechanisms, cardiac effect on local blood flow, and the coupling of extrinsic factors (cardiac and respiratory) to local blood flow by myogenic mechanism. In the control group, local scaling exponent, α(L)=0.96 ± 0.08, did not change but cardiac scaling exponent, α(C)=1.53 ± 0.05, for baseline signal was increased to α(CT)=1.73 ± 0.10 and cardio-respiratory scaling exponent, α(CR)=0.73 ± 0.19, was decreased to α(CRT)=0.24 ± 0.06 during vasodilatation in response to local heating. However, we found significantly different scaling exponents, α(LT)<1, α(CT) ≥ α(C)<1.5 and α(CR) ≈ α(CRT)>0.5 in patients with EHT. Our findings suggest that the local regulatory and the cushioning peripheral vascular functions are impaired in patients with EHT, and vascular/microvascular pathology can be evaluated by applying DFA to LDF signal., (Copyright © 2011 Elsevier Inc. All rights reserved.)