Fractal analysis is one of the quantitative modeling of river networks. By determining the fractal dimension of linear structures such as faults, canals, and meandering river paths, one can estimate many of their features (Turcotte D.L. 1992). Fractal of figure, is a component with static geometric patterns that illustrates the general pattern of a phenomena. The first studies to create quantitative, mathematical, and geometric proper models from river network were made by Horton in 1932 and 1945, yet the study of relationship and comparison quantitative parameters with fractal geometry goes back to the last two decades.
2. Study area
The study area consist of 12 watersheds –Holeylan, Doyraj, Tangesazbon, kolm, NazarAbad, Jezman, Vargach, Chomgez, Chaviz, Siagav, JafarAbad, and Ema– from Ilam Province. Table 1 showed that the formation of study area.  
Table1 the details of formations in the study area.
Formation name Symbol Lithology Sensitivity to erosion of 10
Quaternary Qal Alluvial deposits of the platform 1
Quaternary Qt Alluvial fan 5
Aghajari Aj Sandstone – marl – sandy limestone - conglomerate 6
Gachsaran Gs Marl – limestone marl 3
Asmari Sb Karstic limestone - dolomite 9
Pabdeh Pd Mliky gray shale and marl with limestone 7
Kashkan Kn Conglomerate and sandstone and siltstone red 9
Ahak Tele Zang Tz The average white to cream-colored limestone marl layers 9
Amiran Am Siltstone and sandstone olive to dark brown color 7
Ahak Imam Ehm Rifi fossils of cream-colored limestone with interlayers of Chile 8
Sarvak Sr Thin layer of limestone 9
Ilam Il Medium to thin and milky gray limestone layer 7
In table (1) by increasing the numerical value of resistance degree, the formation sensitivity to erosion is reduced. (Rosovski van Voyk, 1992).
In FayzNiya’s classification (1995) which is based on Rosovski’s classification, rocks with greater resistance have higher value (max 20), and rocks with lesser resistance have lower value (min 1). Therefore, resistance range to erosion of the existing formations in the study areas can vary from 1 to 9.
3. Research Extraction of drainage network via Arc GIS
These networks were provided based on 50 DEM coordinates that in many cases, there isn’t enough accuracy and some channels are not displayed. Therefore, after transferring data to Google Earth, it was fully matched with the natural drainages and with a 5-meter accuracy, hydrographic network map was drawn and completed to reflect the full details of the network.
Thence one cannot scale maps via “Fractalys”, fields with the same space of 25 kilometers on similar formations in different areas were accidentally chosen via “Fish Net” –in Arc GIS, to fix this problem. For each study formation, three 25sq.km. Fields were chosen and by the accuracy of 5 meters. These maps that had the same drawing accuracy and space, were drawn in the same scales via GIS on an A4 page in “.bmp” and then were brought to Fractalys and finally, their fractal dimensions were calculated and extracted by the geometric method of counting boxes.
4. The The results show that a canal with an accuracy of 50 DEM meter on corresponding 5x5sq.km. plots, has much less accuracy than 5 meters in comparison to the drainage network drawn via Google Earth with less than a 5-meter accuracy, and in formations that are sensitive to the formations which are resistant to density changes of the hydrographic network, and have more changes in their fractal dimension as a result.
Google Earth images below are the examples of 25-kilometer areas which their hydrographic networks were revised.     Quaternaryn Gachsaran
Fig 6 modified hydrographic network of 25 km in Google Earth
Fig (6) Regression numeric index to erosion resistance (Sf) and formations fractal dimansion (Fr) after modification of 25 km units
In Fig (6) the amount of R2 is 0.9742 and shows the high correlation and significant relationship of fractal dimension to numerical index for resistance to erosion. by increasing the resistance of the formaion, numerical value of fractal dimension will be decreased.
Table 3 showed that statistical analysis between SF and FR.   Table 3 formations resistance data correlation (from 20) (Sf) and fractal number (Fr) of formations after correcting the 25-kilometer units in them.
Fr Sf
-965.0 000.0
12 1
12 Sf Pearson
Correlation
Sig. (2-tailed)
N
1
12 -965.0 000.0
12 Fr Pearson
Correlation
Sig. (2-tailed)
N
Table (3) shows the amount of data correlation (-965). Their amount would always be between the numbers +1 and -1. The more close its absolute gets to 1, the correlation will be higher, and the more close it gets to zero, the data correlation will get lower. (Ismayili and Kheyri 1385) As a result, there is a meaningful connection between formation resistant and fractal dimension. The minus sign indicates a negative data correlation (Afshani 1387).
Table 4 Regression of the formation resistance values (Sf) and fractal number (Fr) of the areas after the 25-kilometer unit correction
Model Summary
Std. Error of the Estimate Adjusted R Square R Square R Model
0.05116 0.924 0.931 0.965a 1
.
In the table above, “R” is the correlation intensity and its value are always between zero and +1 and “Square” is the coefficient of determination. The more closer “R” value gets to 1, the higher the correlation is between two variables. Therefore the number 0.965 illustrates high correlation of the formatuion resistance and its fractal number.
Total The results show that between the fractal dimension and hydrographic network, there is a significant and negative correlation. The highest amount of fractal dimension in study areas is for the Quaternary formation of granule, equals to 1.65, and the lowest numeral amount of fractal dimension belongs to “Sarvak” formation –equals to 1.06.
Also in formations with greater sensitivity than resistant formations after the correction of the hydrographic network via Google Earth, more changes occurred in the hydrographic network congestion, thereupon their fractal dimension change is also observerd more

Many natural phenomena have many variables that make it difficult to find relationships between them using common mathematical methods. This problem, along with the impossibility of measuring all elements of nature, has led to a major evolution in the way of understanding and explaining phenomena. In this way, one can use the fractal geometry with the theory that many natural phenomena are order in the chaos. Each element of nature is represented as a fractal geometry number. In fact, fractal geometry is a quantitative tool for studying the geomorphology of drainage networks and modeling many complex natural phenomena. Since geological variables have a profound effect on the nature and activity of the drainage networks. In this study, the role of lithology and geological formations is studied to quantify the drainage networks and used fractal dimension to indicate sensitivity to erosion of the formations of this area.

The present study consists of four main sections. The first section is the collection of maps and data. In this section, geological maps of 1:100000 areas were provided and selected from the geological formations of Yazd- Ardakan basin, three geological formations of Kahar, Granit and Taft. Sensitivity to erosion of these formations was studied in this area using PSIAC, Feyznia and Selby methods. In second section, fractal dimension is estimated in 30 plots of 1 × 1 km2, three geological formations of Kahar, Granite and Taft. In each geological formation, fractal dimension was calculated by box counting method using Fractalyse software and the number of plots required in each formation was determined using Graphical method. In the third section of this study, morphometric indices were calculated including drainage density, number of ranks, average length of rank and rank frequency. In the final section, uncertainty analysis of fractal dimension efficiency was studied in classification and separation of geological formations. In most studies in the field of fractal dimension, the uncertainty of this method is not considered. As a result, their findings do not have enough accuracy to generalize to natural phenomena. Therefore, in this study, uncertainty of fractal dimension efficiency was investigated in 30 plots of 1 × 1 km2 that were excluded from other study sections for testing this method.

The mean fractal dimension of 1.149 represents Taft formation, the mean fractal dimension of 1.161, is Granite formation and the amount of 1.207 is Kahar formation. The highest fractal dimension was calculated in Kahar formation (1.279) and the lowest in Taft formation (1.046). In addition, the correlation coefficient is 99%. The results also indicated a significant and meaningful relationship between fractal dimensions of drainage networks and morphometric properties. In this paper, a positive relationship is observed between morphometric parameters and fractal dimension, so that the greatest correlation coefficient is found between the fractal dimension and the drainage density (0.99). The results of uncertainty analysis of fractal dimension showed which fractal dimension in the geological formation of Kahar with 90% has a steady trend and in two geological formations of Taft and Granite, this amount is about 70%. Therefore, fractal dimension in the drainage network identification of the Kahar formation is more powerful than two other granite and Taft formations.

The drainage networks are the most prominent landscapes on earth that are the basis of many hydrological and geomorphological models. Due to the geomorphological characteristics of the region, the drainage network shows its own fractal properties that are saved as code in it. In fact, drainage networks are fractal phenomena with fractal behavior. In this study, the fractal dimension and morphometric properties of the drainage network were used to analyze the sensitivity to erosion of the geological formations of this area. PSIAC and Feyznia methods did not perform well in separating the sensitivity to erosion of Taft and granite formation, and they are unable to distinguish between these two formations. So, using the Selby method, six effective factors were investigated on the resistance and sensitivity of formations to erosion (Schmidt Rebound Hardness, weathering, distance between joints, direction of the joints relative to the slope, the width and connection of the joints) in Taft and Granite formations. The study of these factors leads to field visits and spends a lot of time and cost. As the results of the resistance to erosion of formations were shown by Selby method, Granite formation has less resistance to Taft formation. Due to the climatic conditions in this area, Granit formation is susceptible to weathering. Extreme weathering acts as arenization process. In fact, fractal dimension in three geological formations of the study area is well showed the difference in resistance to erosion of both Taft and Granite formations. The results of this study showed that fractal dimension allows for a quick and accurate analysis of the erosion characteristics and sensitivity to erosion of the formations of this area.

Different natural phenomena have many variables that make it difficult to find relations among them using common mathematical methods. This problem, along with the impossibility of measuring all elements of nature, has led to a major evolution in the procedure of scrutinizing and explaining. In this way, we can use the fractal geometry with the theory that the order of many natural phenomena is chaotic. Fractal geometry is a quantitative tool for studying the geomorphology of drainage networks and modeling many complex natural phenomena. In fact, geophysical phenomena such as basins are fractal phenomena with fractal behavior. An understanding of geomorphologic characteristics and their performance over basins is very important in the watershed management. This paper focuses on the relationship between fractal dimensions of basin shape and drainage network with the geomorphologic characteristics of basin. Therefore, through an analysis of fractal dimensions and its comparison with geomorphologic characteristics, the fractal behavior of this basin is investigated.

The present study consists of four main sections. The first section is the collection of maps and data. In this section, topographic maps at scale of 1:50000 and geological map at scale of 1:100000 from area were provided. Then, the required layers were extracted from them such as drainage networks and geological units. Sensitivity to erosion of formations was studied in this basin using PSIAC method. In order to investigate more precisely, the Aqda was divided into nine hydrological sub-basins (independent), five non-hydrological sub-basins (dependent) and four hybrid sub-basins. The second section, 18 geomorphologic characteristics were calculated for each sub-basin. In the third section of this study, fractal dimension of drainage networks and basin shape was calculated by box counting method using Fractalyse software in each sub-basin. The focus of the final section is on the relationship between fractal dimensions of basin shape and drainage network with the geomorphologic characteristics of basin.

The results showed that the T8 and To3 sub-basins, respectively, with values of 1.47 and 1.60 have the highest fractal dimensions of the drainage network. Also, the highest fractal dimensions of the basin shape were obtained with values of 1.05 and 1.08, respectively, in the same sub-basins (T8 and To3). The results also indicated that there were significant relations among the fractal dimensions of the basin shape and the drainage network with geomorphologic characteristics. The highest correlation belongs to the regression relations between the total length of stream, basin area and erodible area with the fractal dimension of the drainage network (0.98, 0.97 and 0.95 respectively). Fractal dimension of the basin shape showed the highest correlation of 0.82 and 0.8 respectively with the number of networks and the total length of stream (significant at 99 percent level). Then, the erodible status in Aqda Basin was determined by studying the geomorphologic characteristics and comparing it with the fractal dimensions of the basin shape and the drainage network. The highest erodible status is in T8, T1, T6 and TO3 sub-basins which should be considered in strategies to manage Aqda basin. In fact, this study showed that fractal dimensions allow a quick and accurate analysis of the geomorphologic characteristics of the basin and the drainage network.

Identification, evaluation and prioritization of different areas can produce valuable information for the watershed comprehensive plans, soil conservation and mitigation of the erosion types based on amount of erosion and sedimentation. For this purpose, the geomorphologic characteristics should be investigated in basins. But extraction of these characteristics and estimation of the erodible status in basins are time-consuming and costly. Therefore, it is very necessary to use an index that has an appropriate estimation of the erodible status in basins. Fractal dimension, with time and cost management, can determine sensitive and high priority basins. With knowledge about the relationship between geomorphologic characteristics basins with fractal dimension, we can predict the other characteristics of basin. The results of this study indicated that there were significant relation between the geomorphic characteristics of sub-basins study and fractal dimension of the basin shape and the drainage network. Other researches on fractal dimension analysis have shown that there is a significant relation between fractal dimension and characteristics such as basin shape, area, branching ratio, drainage density and length ratio of drainage network. But in this study, two characteristics of branching ratio and length ratio of drainage network were not significantly correlated with any of the characteristics and fractal dimensions, and the drainage density was correlated only with frequency rank. Therefore, basins with high erosion will not always have high drainage density. For example, quaternary alluvial deposits have high erosion, but their drainage density is not very high (T4 sub-basin). For this reason, in the future studies, it is better to separate the tectonic streams from the erosion streams. Finally, the results of this study can confirm the findings of other researchers that fractal dimension of drainage network reflects the complexity of the basin shape and can be used as a quantitative index for basin analysis and evolution of the basin.

The drainage networks as the most prominent landscapes on earth are basis of many hydrological and geomorphological models. Due to the geomorphological properties of the region, the drainage network shows its own fractal properties that are saved as code in it. In fact, drainage networks are fractal phenomena with fractal behavior. Fractal dimension is a parameter used to indicate the complexity of data. The analysis of fractal dimensions of drainage networks and their morphometric properties facilitate the perdition of their behavior in the future. This paper focuses on the relationship between fractal dimensions of drainage networks and their morphometric properties of drainage networks in Yazd- Ardakan basin. Therefore, through an analysis of fractal dimension of drainage networks and its comparison with morphometric properties, the fractal behavior of these drainage networks are investigated. Results showed Pck and Ktl formations indicate highest and lowest fractal dimension respectively. The results indicated a significant relationship between fractal dimensions of drainage networks and morphometric properties. In this research, a positive relationship was observed between morphometric parameters and fractal dimension, so that the greatest correlation coefficient was found between the fractal dimension and the drainage density (0.99).

Fractal art can be presented in simple, reproducible language that is at the same time orderly in the postmodern world. In fractal art, such as visual arts, visual elements such as dots, lines, surfaces, etc. have been used to combine and repeat them and have been expressed in complex shapes and beautiful visual textures. Fractal is an interdisciplinary art related to geometry and mathematics and plays a major role in today's world. It should be said that fractal knowledge makes a unique design possible for the artist. This study intends to investigate the role of fractals in Iranian cultural symbols. In this research, we seek to find fractal applications in signs and with the concern of the audience and the nature of naturalism of art, how can effective and practical solutions be obtained from fractal geometry and new visual patterns in interaction with the audience. The purpose of this study is to get acquainted with fractal geometry and its effect on art; through analysis, adaptation and scientific studies on this geometry, new and practical designs of signs could be achieved. The question arises in which part of art, the traces of fractal geometry can be seen more and it seems that fractal geometry as one of the important tools with a scientific basis in the direction of graphic art can be used more. The research method of this research is descriptive-analytical and the method of collecting information in the form of documents and specific sources about fractals and signs is scattered and more in the form of articles. Fractal has the ability to be widely used as a theoretical basis in logo design.

Soil erosion is a global problem that reduce soil fertility and water quality Proper evaluation of the factor’s affecting erosion is the first step in choosing solution to reduce and control this destructive phenomenon. Important parameters that can be examined in this issue are soil texture, size and quality soil grains and type of bedrock, which can affect the soil erodibility coefficient. Fractal dimension (Df) of particle size distribution (PSD) and fractal dimension of aggregate size distribution (ASD) have been introduced as a predictor of soil texture-related properties. The purposes of this study were to investigate the relations between fractal dimension and various forms of erosion, including surface erosion, rill and badland, also to investigate the relations between fractal dimension and various forms of bedrock and to study the mean weight diameter (MWD), aggregate stability (AS) and aggregate degradation (PAD). Fractal dimension was computed by Yong and Crawford model using the data of particle size distribution experiments by the method of wet and dry sieve and aggregate size distribution by submerged sieve method. Bulk density by weighted method and specific surface area by EGME method were determined. The results of statistical analysis showed that different forms of erosion and bedrock are related to the fractal dimension. In other words, with the development of the erosion form, the fractal dimension increased, so badland had the highest and surface erosion had the smallest fractal dimension. Also, among various bedrocks, with decrease in resistance and increase in erodibility, Df was increased. In addition, fractal dimension had a positive correlation with MWD and AS and negative correlation with PAD. Finally, it can be concluded that due to the ease of calculating the fractal dimension of soil and its proper relationship with erosion, this index can be used in the quantitative and qualitative assessment of soil erosion.

Density current is caused by a slight density difference with the environmental fluid. These currents are of two-phase current type. These currents are non-linear in nature, which are complex and sensitive to initial conditions. Fractal geometry is used as a powerful tool to investigate geophysical phenomena including density current and many complex natural phenomena. This study aimed to conduct a comprehensive study on the fractal and multi-fractal properties of density current and established a significant relation between the Richardson number evolution and the entrainment of ratio density current through fractal analysis. For this purpose, three experimental models in 28 different states were performed by changing the bed slope, density and inlet discharge. The developed codes in MATLAB were used to calculate the multi-fractal generalized dimension indices D(q), singularity spectrum f(α), singularity angle α, the scaling exponent T(q) and fractal dimension Df. The results and various investigations indicated that the fractal dimension decreased a little with the increase of flume bed slope. Further, the fractal dimension increases with increasing the concentration and current discharge. As the Richardson number increases, the scaling exponent has a linear pattern. Furthermore, the fractal dimension changes are monotonic than q in these experiments, and the singularity angles are larger with less range. A significant relationship with 92% coefficient was made between Richardson number and entrainment ratio by fractal analysis.

Particle size distribution (PSD) is one of the sediments' most important physical properties, affecting other physicochemical properties. Fractals are the objects or processes that show a similar appearance or behavior on some large, spatial, or temporal scale. Each fractal can be divided into several parts, each of which resembles the main body. Many natural phenomena and processes are based on fractal models. Loess particles maintain good self-similar properties even when modified through pedogenesis so that the fractal dimension of their particle size is considered as a new indicator of particle size. The loess sequences, produced by aeolian under the influence of past weather changes, have been transported, deposited, and undergone many changes by pedogenesis, whose information is recorded in loess particles. By studying the PSD loess, which is a natural fractal, one can discover data about the past environment. Therefore, PSD changes can be used to indicate the pedogenesis intensity and process or the soil age.Post-depositional pedogenesis, including chemical and biological weathering, causes further particle crushing, the extent of which may vary in different locations due to deposition PSD and the time and intensity of pedogenesis or some other factors. Typically, intense pedogenesis or poor to very poor sorting occurs in warm and humid climates, while poor pedogenesis occurs in cold and dry climates. Changes in the loess texture reflect its post-deposition conditions. Thus, this study sought to analyze Golestan's loess texture developments via fractal PSD for the first time, which could interpret the extent of tissue changes at different points. The results were then compared to the fractal geometry obtained from the electron microscope images.

This study was conducted in Golestan province. The study area is located at latitudes of 38° 8' to 36° 30'N and longitudes of 53° 57' to 56° 22' E. Based on three types of loess texture, including sand loess, silt loess, and clay loess, sixteen samples were totally collected from three zones. Moreover, the fractals were measured using differential box-counting and PSD. The PSD fractal was calculated by sieve-hydrometric (DbH) and laser (Dbl) methods.

The mean DbH for region 1 was 2.64  and region 2 was 2.30. DbH in region three differed in two values. For two regions S12  and S13, the values of DbH are 2.74  and 2.70 and for S 14, S15 and S16 are 2.62,1.06 and 2.24 respectively. Also, the results showed a mean of 4.37 microns and sorting is very poorly (mean φ = 2.96) for region one, a mean of 14.35  microns and sorting is very poorly (mean φ = 3.17) for region two and  a mean of 49.56 microns with two different sorting values show very poorly sorting (mean φ = 2.28) at S13 and S12 stations and sorting poorly (mean φ = 1.78) at stations S16, S15, S14  for zone three. The average fractal grain dimension in region one is 0.673  in region two is 00.788  and in region three is 0.850.. The fractal dimensions of the grain surface in region one have an average of 0.51  in region two is 0.49  and in region three is 0.50. The average value of fractal geometry of grain density arrangement (DFf) is 1.94  in region one, 1.87 in region two and 1.91 in region three.The average fractal arrangement of pore fabric density (DFp) in region one is 1.47  in region two and 1.5  in region three is 1.59.. The fractal geometry of the cement fabric density arrangement is 1.33  in region one, 1.43 in region two and 1.52 in region three.

The results of examining DbH dimensions in the loess of Golestan province show that the percentage of sand decreases and the clay content increases with the increase of DbH. Comparison of fractal with sediment textual parameters indicate that the number of sorting increases and the sorting of particle decreases with the increase of DbH. This means that the samples have a better gradation of PSD and a larger volume of particle size classes. The kurtosis index decreases with the increase of DbH and the curvature broadening increases as a result of the increase of the particle size classes.The results of examining DbL fractal dimensions in the loess of Golestan province show that the percentage of sand decreases and the silt and clay contents increase with the increase of DbL. Based on the results of laser sizing, the increased silt and clay contents lead to a better gradation of sediments. The negative trend of particle sorting against DbL means that the sorting index decreases and the particle sorting increases with the increase of DbL. The positive trend of kurtosis against DbL means that the kurtosis index increases and the curvature broadening decreases with increase of DbL.Three stations of AlmaGol, AlaGol and Agh Ghala Belt in zone 3 had lower DbH and DbL, better sorting, and the highest median size. This may be due to the differences in the sediments’ origins or forming environment and retransfer. This implies that the fractal values ​​can be useful for identifying the transfer mechanism in different sediments.The fractal geometry changes with the changes in loess texture. Therefore, a higher fractal dimension content indicates a higher soil formation and higher fine particle ratios. According to the results, if particle distribution is well graded, it can be claimed that fractal geometry demonstrates the changes after loess deposition. According to the fractal results obtained from electron microscope images in Golestan loess, the fractal dimensions of the grain increased with the increase of diameter. This confirms that near the source, grains are deposited with higher order and away from the source, the fractal number becomes smaller as the grain size decreases. The fractal dimensions of the grain decrease with the increase of particles roundness from zone 3 (near the source) to zone 1 (away from the source). This implies that the sedimentss order decreases and the texture undergoes less changes with the increase of particles roundness. On the other hand, the fractal grain dimensions increase with the increase of sphericity. Since the sphericity decreases from zone 3 to zone 1, the fractal number of grain dimensions decreases. This means that a higher sphericity leads to a higher initial order of the sediment and less texture exposure to changes.The fractal geometry values ​​of the grain fabric density of the fabric in different parts of Golestan province are not equal. Zones 3 and 1 have a higher order than zone 2. Zone 3, with the fractal number close to 2, has a high order during the deposition due to its proximity to the source. In zone 2, with a farther transfer, the particles have been highly subjected to changes in size and arrangement, and thereby the fractal number and order have been subjected to changes and decline. The highest fractal number is seen in zone 1. This can be due to the humid climate in zone 1, which induces the formation of secondary clay and increases the fractal numbers and sediment order. These results show that the content of clay can determine the order and homogeneity of the sediment texture. It can be concluded that fractal and its related parameters, as an efficient tool in analysis of loess sediment, can justify the zone of texture changes, distance from the main source, pedogenesis and climate and The results of DbH dimensions analysis in Golestan province's loess showed that the percentage of sand decreased, and the clay content increased with an increase in DbH. Comparing the fractal with textual sediment parameters indicated that the number of sorting increased and the particle sorting decreased with an increase in DbH, suggesting that the collected samples had a better PSD grading and a larger volume of particle size classes. Moreover, it was found that the kurtosis index decreased with an increase in DbH, and the curvature broadening increased with an increase in particle size classes.The results of Dbl fractal dimensions analysis in Golestan loess showed that the percentage of sand decreased, and the silt and clay contents increased with an increase in DbL. Furthermore, according to the results of laser sizing, the increased silt and clay contents led to a better sediments gradation. A negative trend of particle sorting against DbL means that the sorting index decreased and the particle sorting increased with an increase in DbL. on the other hand, a positive trend of kurtosis against DbL means that the kurtosis index increased and the curvature broadening decreased with an increase in DbL.Three stations, including AlmaGol, AlaGol, and Agh Ghala Belt in zone 3, had lower DbH and DbL, better sorting, and the largest median size, which could be due to the differences in the sediments' origins or the environment's form and retransfer, implying that the fractal values could help identify the transfer mechanism in different sediments.The fractal geometry would change with the changes made in loess texture. Therefore, a higher fractal dimension content indicates a higher soil formation and higher fine particle ratios. According to the study's results, should the particle distribution is well graded, it can be claimed that fractal geometry demonstrates the post-deposition changes in the loess. Based on the fractal results obtained from electron microscope images in Golestan loess, the grain's fractal dimensions increased with an increase in diameter, indicating that the grains are deposited with higher-order near the source, and the fractal number becomes smaller with the decrease in the grains' size away from the source. It was also found that from zone 3 (near the source) to zone 1 (away from the source), the grains' fractal dimensions decreased with an increase in particles roundness, implying that the sediments' order decreased and the texture underwent fewer changes with an increase in particles roundness. On the other hand, the grains' fractal dimensions increased with an increase in sphericity. Therefore, as the sphericity decreased from zone 3 to zone 1, the fractal number of grain dimensions decreased too, indicating that higher sphericity led to a higher initial order of the sediment and less texture exposure to changes.The fractal geometry values of the grain's fabric density in different parts of Golestan province are not equal. Therefore, zones 3 and 1 had a higher order than zone 2. Due to its proximity to the source, zone 3, with the fractal number close to 2, had a high order during the deposition. In zone 2, with a farther transfer, the particles were highly subjected to changes in size and arrangement, and thereby the fractal number and order were subjected to changes and decline. Moreover, zone 1 was found to have the highest fractal number because of its humid climate, inducing secondary clay formation and increasing the fractal numbers and sediment order.These results suggest that the content of clay can determine the order and homogeneity of the sediment's texture. Therefore, it can be concluded that as an efficient tool in analyzing loess sediment, fractal and its related parameters can justify the zone of texture changes, distance from the main source, pedogenesis, and climate, and determine the model of post-deposition changes.

Since there are not enough tools to measure flood, erosion and sediment in many watersheds of the country, it is necessary to use indirect methods such as fractal geometry to estimate them. There is very little accurate information about erosion in our country (Mohammadi et al. 2008). Understanding the sedimentation status and sedimentation of basins provides an accurate understanding of erosion and its consequences (Piri et al. 2005). Some parameters of watersheds have a special geometric shape that can be examined with fractal geometry. Mathematically, the basins that have the same fractal dimensions are equivalent to each other and are very similar in terms of geomorphological and hydrological characteristics (Adl and Mehrvand, 2004). The aim of this study is to obtain a significant relationship between fractal drainage network and erosion and sedimentation rates, and to generalize the results to unmeasured areas. 2. Introducing the studied area The studied area consists of 12 basins of Ilam province, which are in the western foothills of Zagros Mountain. Figure 1- The position of studied basins in the country and in the Ilam province Table 1- Specifications of basins and their stream gauging stations

These networks were provided based on 50DEM coordinates that in many cases, there isn’t enough accuracy and some channels are not displayed. Therefore, after transferring data to Google Earth, it was fully matched with the natural drainages and with a 5-meter accuracy, hydrographic network map was drawn and completed to reflect the full details of the network.Thence one cannot scale maps via “Fractalys”, fields with the same space of 25 kilometers on similar formations in different areas were accidentally chosen via “Fish Net” –in Arc GIS, to fix this problem. For each study formation, three 25sq.km. Fields were chosen and by the accuracy of 5 meters. These maps that had the same drawing accuracy and space, were drawn in the same scales via GIS on an A4 page in .bmp” and then were brought to Fractalys and finally, their fractal dimensions were calculated and extracted by the geometric method of counting boxes.

Figure 2- Hydrographic network and fractal dimension of the nazarabad watersheds before hydrographic network modification Table 2- Fractal dimension of watersheds before and after hydrographic networks modification In the following figures, the calculated fractal dimensions are observed for several samples of 25 km units before and after the hydrographic network modification. After the modification before the modification Amiran Aghajari 1.134 1.481 1.149 1.435 Figure 3- Fractal dimension of a hydrographic network of Aghajari and Amiran formations before and after hydrographic network modification. Quaternery Gachsaran Figure 4- Hydrographic network modification in the 25km unit on Google Earth Figures (3) to (4) show that after hydrographic network modification, the density of the hydrographic network and consequently the fractal dimension are increased in units of 25 km. Also, hydrographic network density changes in more sensitive formations are more than resistant formations, so their fractal dimension changes are also higher.Figure 5- Investigating the correlation of fractal dimension with hydrological indexes of Ilam watersheds the R2 value that is representing the correlation value is 0.0905. Therefore there is no significant relationship between the specific flood discharge of watershed and its fractal number. Table (3) Correlation test of specific flooddischarge data (Qw) in terms of (m3/s/ Km2) and fractal number (Fr) of the basins after modification of 25km units In Table 3, the specified number (-.240) indicates the correlation value of the data. Due to the obtained value, there is no correlation between the specific flood discharge and the fractal number of the basin.Figure 6- Correlation line chart of specific flood discharge data and fractal number of basins after modification of 25km un its Figure 7- Investigating the correlation of fractal dimension with the sedimentation index of Ilam watersheds In Figure 8, Due to the R2 value (0.939), it can be also concluded that there is a significant and direct correlation between the specific sediment discharge value and fractal dimension of the watershed. The following tables show the results of the calculations performed in SPSS software. Table 4- Correlation test of specific sediment discharge data (Qs) and fractal number (Fr) of basins after modification of 25km units The results of SPSS in Table (4) show that there is a high correlation between the specific sediment discharge data and fractal number. Because the number of 0.996 equals the correlation value between the two variables of the specific sediment discharge and the fractal dimension of the basins. The dispersion of data in the figure represents a high correlation in the data. Because the data are not scattered.

The fractal dimension gives more accurate results by the box-counting method than the magnification and radial methods..The results of the research show that there is a significant and inverse relationship between the fractal dimension of the formations and their resistance to erosion.As the strength of the formation increases, its fractal dimension decreases and therefore the density of the hydrographic network is lower.There is no regular trend between the hydrographic network density and the fractal dimension of the basin with the specific flood discharge of basins.Also, there is no significant relationship between this index and the fractal dimension of the basin.There is a significant and direct relationship between the fractal number and the specific sediment discharge (at a level of 5%), which indicates the erosion and roughness rate in the basin The highest value of fractal dimension can be observed in areas that are very sensitive, including Doiraj basin to 1.49.The least value of fractal dimension can be observed in areas that are resistant to semi-resistant in terms of geological formations, such as Kolm and Chamagaz equal to 1.14 and 1.11, respectively.

Digital elevation models and its derivatives are important factors for watershed modeling. It is obvious that DEM errors adversely affect the accuracy and thereby modeling of natural processes. This problem along with the impossibility of measuring all elements of nature, has led to a major evolution in the way of understanding and explaining phenomena. In this way, we can use the fractal geometry as a quantitative tool for modeling many complex natural phenomena. In fact, geophysical phenomena such as drainage networks are fractal phenomena with fractal behavior. The purpose of this paper is to evaluate sensitivity of the drainage networks based on DEMs (ASTER & SRTM), flow direction algorithms (Single Flow Direction (D8) and Multiple Flow Direction (MD8)) and topographic maps of 1:25000 in order to study the fractal dimension of drainage network on geological formations of Yazd-Ardakan basin. The results showed that the least difference in the length and the rank of the stream belonged to the drainage network obtained from the topographic maps of 1:25000. After the topographic maps, ASTER and the multi-flow direction algorithm are close to real ground map. Even though the multi-flow direction algorithm shows more detail on the drainage network. But it is not close to real ground map. The difference is particularly noticeable in the first rank of streams. Due to the very high sensitivity of the fractal dimension to the smallest change in drainage network conditions, the drainage network obtained from topographic maps were used to calculate the fractal dimension. The mean fractal dimension of 1.149, 1.16 and 1.207, respectively, represents Taft, Granite and Kahar formations. There is a significant correlation between fractal dimension and sensitivity to erosion of geological formations (level 0.99). In fact, the fractal dimension increases with increasing the sensitivity to erosion along with the drainage density in geological formations. The results showed that fractal dimension allows for a quick and accurate analysis of sensitivity to erosion of the formations of this area.