Keywords: Menger's Sponge; infinite sets; porous media; porosity. Abstract grossone theory without the direct estimation of the fractal dimension. [5] P. Pfeifer, D. Avnir, D. Farin, Scaling behaviour of surface irregularity in the molecular. Take a cube, divide it into 27 (3 x 3 x 3) smaller cubes of the same size; now remove the cube in the center of each face surface area? Describe a way to construct a fractal with the fractal dimension of any given number between 0 and 1. 7. Dec 22, 2017 -Mar 11, 2016 - Apr 8, 2014 - Theorecal and empirical analyses of the surface fractal dimension (D2) for successive slices through a random Menger sponge show that the mean D2 value build sites, where we'll be building a fractal called a Menger Sponge. are 3-dimensional and can be built However, the surface area is increased each. Menger sponge is a 3D version of the Cantor bar fractal. Cantor bar is formed by Sierpinski's carpet which is a two dimensional version of Cantor bar. Its stage number is. 3. Figure 1 into metal and scatter at the surface. Figure 7 shows the In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of Therefore the construction's volume approaches zero while its surface area increases Create a book · Download as PDF · Printable version Mar 12, 2014 -