Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension Df 1⁄4 2:15 0:15. We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is \2.3. A kinetic model of sandblasting is presented, which...

In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

In the present paper, the bounds on fractal dimension of Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) in R on a equispaced mesh are found. These bounds determine the conditions on the free parameters for fractal dimension of the constructed CHFIS to become close to 3. The results derived here are tested on a tsunami wave surface by computing the lower and upper bounds of th...

The present work describes the evaluation of the conventional roughness parameters and fractal dimensions of the surface profiles generated by turning of brass with different machining conditions such as depth of cut, work-piece speed and feed rate. The surface roughness parameters on the generated-turned surfaces were measured with a stylus-type profilometer and processed through the dedicated...

Background:Leukemia is cancer of blood and bone marrow cells. In general, there are four types of leukemia: chronic myelogenous leukemia (CML), acute myeloid leukemia (AML), B-cell chronic lymphocytic leukemia (CLL) and acute lymphoblastic leukemia (ALL).  Fractal geometry can be introduced as one of the effective ways to detect this type of cancer. In this study, with introduc...

introduction: soil hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. in recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (ks). fractal models with two subset of two (solid and pore) and three phases (solid,...

The surface analysis of nanomachined AISI D2 tool steel materials is measured using atomic force microscopy. The surface roughness and fractal dimensional analysis are the important factors in nano tribology and evaluating the quality of nanomachined surface. Carbon nanotube increases the heat carrying capacity, thermal conductivity of the lubricating oil and thus prevents any damage to the wor...

In order to strengthen the prediction of rockburst and inquire the relationship between the rockburst proneness of rock and its surface fractal characteristic, the surface fractal of the rock was studied by fractal method and uniaxial compression test. The change rules of surface fractal of different types of rock were compared by calculating its fractal dimension of rock before experiment and ...

We have discovered a new fractal pattern, coffee exhibits on a horizontal surface, with a fractal dimension 06 . 0 88 . 1 ± , when a heavy coffee droplet interacts with the surface of lighter milk. Parts of coffee pattern on the surface disappear due to Rayleigh–Taylor instability, and the annihilative behavior produces the fractal pattern. Coffee fractals and the Sierpinski carpet have common ...

introduction: water and soil retention curve is one of the most important properties of porous media to obtain in a laboratory retention curve and time associated with errors. for this reason, researchers have proposed techniques that help them to more easily acquired characteristic curve. one of these methods is the use of fractal geometry. determining the relationship between particle size di...