Order! Order!
Te fractal dimension of sur- faces arising from some types of fracture or wear correlates with the energy absorbed in the pro- cess [13]. Wear on archaic stone tools produces fractal surfaces that indicate the use of the tool (scraping, cutting, etc.). Surface fractal dimension determines how well surface contacts can transmit heat or electricity [14]. Figure 13 shows SEM images of fractal surfaces in 3 dimen- sions formed by erosion and by growth.
Figure 12: Measuring the fractal dimension of Australia based on the Euclidean distance map.
Fiber Arrangements in Two and Three Dimensions One very important field
Figure 13: SEM images of 3D fractal structures: (a) sponge; (b) weathered granite.
in Figure 12 using the coastline of Australia. Measuring the area of a ribbon centered on the coast as a function of the rib- bon width is quickly done by plotting the cumulative values in the Euclidean distance map, which assigns each pixel in the image a value representing its distance from the edge. Similar measurements show, for example, that the Hawaiian Islands generally have an increase in fractal dimension with age, with the youngest being the smoothest [12]. Measurement of the border of tumors shows that higher fractal dimension indicates a greater likelihood of malignancy.
where random, self-avoiding, and highly regular arrange- ments are used for their contri- bution to specific properties is in textiles, both woven and non- woven. Materials constructed of fibers are oſten thin and essen- tially two-dimensional, such as cloth and paper, and may have a high degree of order, be par- tially ordered, or be highly dis- ordered. Te simplest
form of woven cloth consists of orthog-
onal fibers; the interlacing of these fibers usually follows one of several common weave patterns (Figure 14). Te intermixing of different colored threads introduces patterns in the cloth, and advanced techniques, such as Jacquard weaving that com- bine multiple patterns and colors, can produce extremely com- plex designs. Basic weaving has been performed by humans for at least 8,000 years. As shown in Figure 15, fibers oriented in different
directions, either by design or accident, may introduce more irregularity to the pattern. Woven fabrics may have
Figure 14: Some common regular weave patterns, with horizontal weft and vertical warp: (a) plain; (b) basket; (c) twill; (d) herringbone. 16
www.microscopy-today.com • 2020 March
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