1-16 OF 16 RESULTS FOR

Menger sponge fractals

Results shown limited to content with bounding coordinates.
Follow your search
Access your saved searches in your account

Would you like to receive an alert when new items match your search?
Close Modal
Sort by
Journal Article
Published: 01 February 2009
Vadose Zone Journal (2009) 8 (1): 187–196.
.... The Menger sponge is a three-dimensional mass fractal that represents the complicated pore space geometry of soil and rock. Predictions based on the analytical models were compared with estimates of k derived from lattice Boltzmann method (LBM) simulations of saturated flow in virtual representations...
FIGURES | View All (9)
Image
(a) Deterministic <span class="search-highlight">Menger</span> <span class="search-highlight">sponge</span> of unit width and scaling factor  b  = 3, l...
Published: 01 February 2009
F ig . 1. (a) Deterministic Menger sponge of unit width and scaling factor b = 3, last iteration level n = 3, a mass fractal dimension of D 3 = log20/log3 = 2.726… and D 2 = log8/log3 = 1.892… for each face of the cube, and (b) one realization of a randomized Menger sponge with unit
Image
Variation of the <span class="search-highlight">fractal</span> dimension  D  2  through slices of deterministic a...
Published: 01 February 2009
F ig . 2. Variation of the fractal dimension D 2 through slices of deterministic and random Menger sponges with scaling factor b = 3, last iteration level n = 3, and fractal dimension D 3 = 2.726.
Image
Distribution of intrinsic permeability ( k ) from lattice Boltzmann method ...
Published: 01 February 2009
F ig . 8. Distribution of intrinsic permeability ( k ) from lattice Boltzmann method simulations in 100 realizations of the scaling factor b = 3, fractal dimension D = 2.726, and last iteration level n = 3 randomized Menger sponge.
Image
Relationship between the measure of connectivity ( P ) and intrinsic permea...
Published: 01 February 2009
F ig . 9. Relationship between the measure of connectivity ( P ) and intrinsic permeability ( k ) from lattice Boltzmann method (LBM) simulations in 100 realizations of the scaling factor b = 3, fractal dimension D = 2.726, and last iteration level n = 3 randomized Menger sponge.
Image
Log–log plot of three-dimensional relative lacunarities [R ln ( L )] vs. gl...
Published: 01 February 2009
prefractal of a Menger sponge (labeled fractal ) and for the image with small, randomly distributed pores (labeled random ).
Journal Article
Published: 01 February 2009
Vadose Zone Journal (2009) 8 (1): 174–176.
... how natural heterogeneous materials can exhibit both mass- and pore-fractal scaling. Cihan et al. (2009) present new analytical models for predicting the saturated hydraulic conductivity based on the Menger sponge mass fractal. They tested their model predictions against lattice Boltzmann...
Journal Article
Published: 01 February 2009
Vadose Zone Journal (2009) 8 (1): 233–241.
... prefractal of a Menger sponge (labeled fractal ) and for the image with small, randomly distributed pores (labeled random ). ...
FIGURES | View All (7)
Series: Geological Society, London, Special Publications
Published: 01 January 2010
DOI: 10.1144/SP332.2
EISBN: 9781862395800
... of an explanation for the peculiar distributions of volume and diffusion domain radius in published data ( Lovera et al. 1989 , 1997 ). Therefore we used two fractal distributions of volume and diffusion domain size for comparative purposes, the fractal cube (Fig.  2 a) and the Menger sponge (Fig.  2 b...
FIGURES | View All (9)
Journal Article
Journal: Interpretation
Published: 30 June 2021
Interpretation (2021) 9 (3): T747–T765.
... and subsequent depiction of the fractal dimensions of porous rock, four methods should be considered: (1) box-counting image analysis ( Hansen and Skjeltorp, 1988 ), (2) the Frenkel-Halsey-Hill (FHH) model ( Heister, 2014 ), (3) the Menger sponge model ( Krohn, 1988 ), and (4) the Brooks-Corey model ( Brooks...
FIGURES | View All (12)
Journal Article
Journal: AAPG Bulletin
Published: 01 July 2021
AAPG Bulletin (2021) 105 (7): 1491–1509.
... ), where Slope refers to slope. Following the work of Pfeifer and Avnir (1983) , Friesen and Mikula (1987) derived a relation for calculating the surface fractal dimension based on the well-known geometrical fractal model known as the Menger sponge. Its mathematical expression is as follows...
FIGURES | View All (11)
Journal Article
Published: 01 March 2014
European Journal of Mineralogy (2014) 26 (1): 189–198.
... (Giuggiulena Limestone) calcirudite grain-supported Biosparite or grainstone sparite (20 %) Coralline algae (30 %), bryozoans (10 %), bivalves (5 %) Intergranular porosity and secondary sparite dissolution porosity (35 %) Fig. 5 The iterative structure of Menger sponge. Fig. 6...
FIGURES | View All (8)
Journal Article
Published: 01 November 2007
Vadose Zone Journal (2007) 6 (4): 786–792.
... ). The sensitivity of Eq. [8] to the parameters P and D d is demonstrated for a three-dimensional mass prefractal porous medium or Menger sponge in Fig. 2 . Figure 2a shows changes in S as function of log b ( h / h min ) while P is varied from 0.1 to 1 and D d is kept constant at 2.5 (< D...
FIGURES | View All (5)
Journal Article
Journal: AAPG Bulletin
Published: 15 June 2019
AAPG Bulletin (2019) 103 (6): 1297–1319.
...). The fractal dimension calculation using the results of a mercury injection test can be described based on the Menger sponge fractal model ( Hegedus and Pereira, 1990 ; Jarz̧bski et al., 1995 ) and the Washburn equation ( Washburn, 1921 ). During the process of the mercury intrusion test, the mercury could...
FIGURES | View All (24)
Journal Article
Published: 01 November 2005
Vadose Zone Journal (2005) 4 (4): 959–966.
... from a solid initiator by an iterative process of mass removal and re-scaling. As a concrete example, consider the well-known Menger sponge that scales by a constant ratio of b = 3 ( Mandelbrot, 1982 ). The initiator is a solid cube ( E = 3) of unit length. A generator is then defined...
FIGURES | View All (4)
Journal Article
Published: 01 January 2015
Reviews in Mineralogy and Geochemistry (2015) 80 (1): 61–164.
... F Matarrese S Mollerach S ( 1994 ) The 3-point correlation-function of the cosmic microwave background in inflationary models . Astrophys J 430 : 447 – 457 Garrison JR Pearn WC Vonrosenberg DU ( 1993a ) The fractal Menger sponge and Sierpinski carpet as models...
FIGURES | View All (47)