Textural fractal dimension

Borges, A., and Peleg, M. (1996). Determination of the apparent fractal dimension of the force-displacement curves of brittle snacks by four different algorithms. J. Texture Stud., 27,243-255. 

Hence plots of log against log Twill have a slope of -D. The parameter D is characteristic of the texture of the particle and was called by Mandelbrot the fractal dimension. The fractal dimension for the outline of a particle lies between 1 and 2, the more irregular the outline, the higher the value. 

The texture of surfaces can also be described using fractals, the more irregular the surface, the higher its fractal dimension a fractal surface is defined as being a surface in which increasing and similar detail is... 

Fig. 3 Fractal dimensions can be used to evaluate the rugged structure of fine particles. (A) Fractal dimensions used to describe the ruggedness of various lines (B) physical basis of the equipaced exploration technique for evaluating the fractal dimensions of rugged boundaries (C) data generated by the equipaced exploration technique for the profile of (B) c5s, structural boundary fractal dimension c5x, textural boundary fractal dimension.

The critical indices estimated from these relations fall into the admissible ranges of variation P = 0.39-0.40, V = 0.8-0.9, and t = 1.6-1.8, determined in terms of the percolation model for three-dimensional systems. The researchers [7] noted that not only numerical values but also the meanings of these values coincide. Thus the index P characterises the chain structure of a percolation cluster. The 1/p value, which serves as the index of the first subset of the fractal percolation cluster in the model considered [7], also determines the chain structure of the cluster. The index v is related to the cellular texture of the percolation cluster. The 2/df index of the second subset of the fractal percolation cluster is also associated with the cellular structure. By analogy, the index t defines the large-cellular skeleton of the fractal percolation cluster. The relationship between the critical percolation indices and the fractal dimension of the percolation cluster for three-dimensional systems and examples of determination of these values for filled polymers are considered in more detail in the book cited [7]. Thus, these critical indices are universal and significant for analysis of complex systems, the behaviour of which can be interpreted in terms of the percolation theory. 

Although there are fractal systems in the environment which are not aggregates, such as the fractal surface roughness of fractures and wear particles, the texture of clouds and the distribution of stars in the night sky, these are less often of interest in the study of environmental systems. Surface fractal dimensions are also considered important in environmental systems and, although they are subject to many of the same principles discussed later, are not treated explicitly here. 

Kovalsky and Bushell speculate that it might even be possible to measure the fractal dimension directly from the texture of the reflected laser [74]. 

Colbeck et al. [88] analysed various smokes and found textural fractal dimensions in the range 1.12-1.27 for petrol, diesel, fuel, oil, paraffin, butane and wood (Table 9.2), whilst the mass fractal dimensions were 2.04, 1.88, 1.97 and 2.35 for diesel, fuel oil, butane and wood respectively. This wide range represents a... 

Despite numerous algorithms and experimental techniques for determining the fractal dimension of aerosols, a quantitative description of atmospheric aerosols is rare. Those which have been reported have involved image analysis of ambient aerosols collected on a Alter or TEM grid [23,101-103]. Kindratenko etal. [102] concluded that fractal analysis allows the unequivocal identiflcation of particles source. For samples from Siberia they quote a textural fractal dimension of 1.09 0.015 for fly ash and 1.04 0.015 for soil. However, the majority of the fly ash particles examined were spherical and did not exhibit any fractality. This suggests that, in this case, fly ash was formed by different mechanisms. 

Kaye BH. Specification on the ruggedness and/or texture of a fine powder profile by its fractal dimension. Powder Technol 1978 21 1. 

Textural Evolution. The textural evolution of aerogels with sintering is usually described using the specific surface area, the porous features (porosity, mean pore size distribution) or the solid phase microstructure (fractal dimension, cluster and primary particle... 

It is rather interesting to note that overall the textural fractal dimensions stays virtually the same. The different structural friictal dimensions have physical significance in that the east and west coasts of Great Britain consist of different rock types and are exposed to different formative processes. The west coast, which has a ru ed profile, is made up of more mountainous material and faces into the storms of the Atlantic. 

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