• Research in Mathematical Education
• /
• v.5 no.1
• /
• pp.1-12
• /
• 2001

Generating fractal images by graphing calculators such as TI_92 combines several important features, which convey the excitement of a living, changing mathematics appropriate to secondary or post-secondary students. The topic of fractal geometry can be illustrated using natural objects such as snowflakes, leaves and ferns. These complex and natural forms are often striking fantastic and beautiful. The examples highlight the fact that complex, natural behaviors can result from simple mathematical rules such as those embodied in iterated function systems(IFS). The visual splendor beauty of fractals, in concert with their ubiquity in nature, revels the intellectual beauty of nonlinear mathematics in a compelling way. The window is now open for students to experience and explore some of the wonder of fractal geometry.

• The Journal of Engineering Geology
• /
• v.4 no.2
• /
• pp.127-138
• /
• 1994

The stationary dual-porosity model is not sufficient to describe the hydraulic characteristics of fractured aquifers as the groundwater flow in fractured aquifers is often controlled by the fractal geometry of fractures. This study deals with new stationary dual-porosity fractal model. This model simulates pseudo-steady state flow from matrix block to fissure in the fractal aquifer. Furthermore, it considers storage capacity and well loss effect at the production well. Type curves for different flow dimensions with different drainage factors are plotted. This new model has been applied to experimental data. The result of the interpretation shows a good accordance between the theoretical model and the observed data.

• Journal of Welding and Joining
• /
• v.18 no.5
• /
• pp.77-83
• /
• 2000

This study proposes the analysis and evaluation method of time series ultrasonic signal using the attractor analysis. Features extracted from time series signal analyze quantitatively characteristics of weld defects. For this purpose, analysis objective in this study is fractal dimension and attractor quadrant feature. Trajectory changes in the attractor indicated a substantial difference in fractal characteristics resulting from distance shifts such as parts of head and flange even though the types of defects are identified. These difference in characteristics of weld defects enables the evaluation of unique characteristics of defects in the weld zone. In quantitative fractal feature extraction, feature values of 3.848 in the case of part of head(crack) and 4.102 in the case of part of web(side hole) and 3.711 in the case of part of flange(crack) were proposed on the basis of fractal dimensions. Proposed attractor analysis and DAC in this study can enhance the precision rate of ultrasonic evaluation for defect signals of rail weld zone such as side hole and crack.

• Journal of Mechanical Science and Technology
• /
• v.15 no.10
• /
• pp.1417-1422
• /
• 2001

Since fracture surface presents clear evidence to describe the circumstances of material failure event, analysis of fracture surface should provide plenty of useful information for failure prevention. Thus if we extract proper information from the fracture surface, the safety evaluation, for plant component could be more accurate. In general, the chaotic morphology of fracture surface is determined by the degree of material degradation as well as by other factors such as type of load, geometry of specimen, notch condition, microstructure of material and environment. In this research, we developed a fractal analysis technology for the fracture surface of aged turbine rotor steel based on the slit-island technique using an image analyzer. Moreover the correlation between the fractal dimension and the aging time was studied.

• KIEE International Transactions on Electrophysics and Applications
• /
• v.11C no.2
• /
• pp.18-22
• /
• 2001

The thin films of high permitivity in ferroelectric materials using a capacitor are applied to DRAMs and FRAMs. (Ba, Sr)TiO$_3$ thin as ferroelectric materials were prepared by the sol-gel method and made by spin-coating on the Pt/Sio$_2$/Si substrate at 4,000 [rpm] for 10 seconds. The structural characteristics of the surface were analyzed by fractal dimension. The thickness of BST ceramics thin films was about 260∼280 [nm]. The property of the leakage current was stable with 10-9∼10-11[A] when the applied voltage was 0∼3[V]. BST thin films ha low leakage current properties when fractal dimension was low and a coating area was high.

• Journal of Biomedical Engineering Research
• /
• v.17 no.3
• /
• pp.305-312
• /
• 1996

A new three dimensional fractal coding is proposed with a perceptually enhanced matching. Since most of medical images (e.g. computed tomoyaphy or magnetic resonance images) have three dimensional characters, searching regions are extended to adjacent slices. For a perceptually enhanced matching, a high frequency boost filter is used for pre-filtering images to be encoded, and a least mean square error matching is applied to the edge enhanced Images rather than the original images. From simulation with magnetic resonance images($255\times255$, 8bits/pixel), reconstructed images by the proposed compression algorithm show much improved subjective image quality with higher peak signnal-to-noise ratio compared to those by existing fractal coding algorithms at compression ratios of about 10.

• Proceedings of the KOSOMBE Conference
• /
• v.1995 no.05
• /
• pp.37-41
• /
• 1995

In this paper, we proposed the 2-stage ultrasound liver image classifier which uses the fractal dimensions obtained from the original image and its 1/2 subsampled image, and the Normalized Fourier Power Spectrum. The fractal dimension based on Fractional Brownian Motion (FBM) is calculated from the variance of the same scale pixels instead of the mean of them. Since the actual ultrasound. liver images does not fully match the FBM, to get the fractal dimension, we use the scale vectors which satisfy the FBM model. In 2-stage classifier, we first classified normal and diffuse liver and then classified the fat liver and cirrhosis from the diffuse liver. For the test liver images. 70% of normal liver and 80% of fat liver and 90% of cirrhosis is classified classified with our 2-stage classifier.

• Proceedings of the KOSOMBE Conference
• /
• v.1995 no.05
• /
• pp.131-134
• /
• 1995

A three dimensional fractal coding with a perceptually enhanced matching is proposed. Since most of medical images (e.g. computed tomography or magnetic resonance image) have three dimensional character, the searching region is extended to adjacent slices. For perceptually enhanced matching, a high frequency booster filter is used for prefiltering of the original image, and the least mean square error matching is applied to this edge enhanced image rather than the original image. From the simulation with the magnetic resonance images ($255{\times}255$, 8bits/pixel). the proposed algorithm provides excellent image quality with compression rations higher than 10. Compared to existing fractal coding the algorithm also provides better subjective image quality with higher compression ratio.

• International Journal of CAD/CAM
• /
• v.8 no.1
• /
• pp.37-40
• /
• 2009

Based on the study of Digital Elevation Simplification Model and fractal theory, this paper put forward a new method to simulate complex terrain. That use simplified DEM data to construct terrain frame based on the quad tree at first, and then use fractal to generate the details of every node of the tree. In the process of construction, the LOD theory is used to simplify the terrain and get its typical data. According to the change of view position and direction, the paper gives a new way to judge the visibility of the surface patch. Experimental results show that this algorithm is simple, efficient and supports the real time dynamic simulation of terrain model.

• Journal of Ocean Engineering and Technology
• /
• v.14 no.1
• /
• pp.29-36
• /
• 2000

Surface micro-crack grows along intergranular or transgranular region of crystal grains. But if it meets the barrier such as sessile dislocation and precipitates it loses straightness and deflects. Investigators had many difficulties in estimating fatigue life of smooth specimen because of the random distribution growth and coalescence of surface micro-cracks. The path of surface micro-crack has irregularity due to nonhomogeneous microstructure. Euclidian geometry can't quantify the shape of surface micro-crack but fractal geometry can. Therefore in this paper fractal dimension is measured at various stage of cycle ratio and estimated cycle ratio in 2024-T3 aluminium, alloy.