A Relative Fractal Dimension Spectrum as a Complexity Measure

2006 ◽  
Author(s):  
W. Kinsner ◽  
R. Dansereau
Keyword(s):  
Fractal Dimension ◽  
Complexity Measure ◽  
Dimension Spectrum

A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure

2011 ◽  
pp. 381-395
Author(s):  
W. Kinsner ◽  
R. Dansereau
Keyword(s):  
Fractal Dimension ◽  
Probability Distributions ◽  
Objective Measure ◽  
Mean Opinion Score ◽  
Perceptual Quality ◽  
Dimension Spectrum ◽  
Opinion Score ◽  
Single Scale ◽  
Scale Measure

This article presents a derivation of a new relative fractal dimension spectrum, DRq, to measure the dis-similarity between two finite probability distributions originating from various signals. This measure is an extension of the Kullback-Leibler (KL) distance and the Rényi fractal dimension spectrum, Dq. Like the KL distance, DRq determines the dissimilarity between two probability distibutions X and Y of the same size, but does it at different scales, while the scalar KL distance is a single-scale measure. Like the Rényi fractal dimension spectrum, the DRq is also a bounded vectorial measure obtained at different scales and for different moment orders, q. However, unlike the Dq, all the elements of the new DRq become zero when X and Y are the same. Experimental results show that this objective measure is consistent with the subjective mean-opinion-score (MOS) when evaluating the perceptual quality of images reconstructed after their compression. Thus, it could also be used in other areas of cognitive informatics.

scholarly journals COMPLEXITY OF THE FIBONACCI SNOWFLAKE

Fractals ◽  
2012 ◽  
Vol 20 (03n04) ◽  
pp. 257-260 ◽  
Author(s):  
ALEXANDRE BLONDIN MASSÉ ◽  
SREČKO BRLEK ◽  
SÉBASTIEN LABBÉ ◽  
MICHEL MENDÈS FRANCE
Keyword(s):  
Fractal Dimension ◽  
Fibonacci Sequence ◽  
Complexity Measure ◽  
Square Lattice

The object under study is a particular closed and simple curve on the square lattice ℤ2 related with the Fibonacci sequence Fn. It belongs to a class of curves whose length is 4F3n+1, and whose interiors tile the plane by translation. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.

Reconstructing the fractal dimension of granular aggregates from light intensity spectra

Soft Matter ◽  
2015 ◽  
Vol 11 (47) ◽  
pp. 9150-9159 ◽  
Author(s):  
Fiona H. M. Tang ◽  
Federico Maggi
Keyword(s):  
Fractal Dimension ◽  
Light Intensity ◽  
Dimension Spectrum ◽  
Capacity Dimension

The 3D capacity dimension d0(S3) of aggregates is retrieved using a 2D perimeter-based fractal dimension spectrum dP,I that varies with image light intensity.

Use of fractals to describe microstructures of porous thick-film platinum electrodes

1992 ◽  
Vol 50 (1) ◽  
pp. 314-315
Author(s):  
Steven D. Toteda
Keyword(s):  
Fractal Dimension ◽  
Power Plants ◽  
Electrical Response ◽  
Cubic Phase ◽  
Platinum Electrodes ◽  
Fine Grained ◽  
Impedance Response ◽  
Platinum Particles ◽  
Energy Surfaces ◽  
Highly Porous

Zirconia oxygen sensors, in such applications as power plants and automobiles, generally utilize platinum electrodes for the catalytic reaction of dissociating O2 at the surface. The microstructure of the platinum electrode defines the resulting electrical response. The electrode must be porous enough to allow the oxygen to reach the zirconia surface while still remaining electrically continuous. At low sintering temperatures, the platinum is highly porous and fine grained. The platinum particles sinter together as the firing temperatures are increased. As the sintering temperatures are raised even further, the surface of the platinum begins to facet with lower energy surfaces. These microstructural changes can be seen in Figures 1 and 2, but the goal of the work is to characterize the microstructure by its fractal dimension and then relate the fractal dimension to the electrical response. The sensors were fabricated from zirconia powder stabilized in the cubic phase with 8 mol% percent yttria. Each substrate was sintered for 14 hours at 1200°C. The resulting zirconia pellets, 13mm in diameter and 2mm in thickness, were roughly 97 to 98 percent of theoretical density. The Engelhard #6082 platinum paste was applied to the zirconia disks after they were mechanically polished ( diamond). The electrodes were then sintered at temperatures ranging from 600°C to 1000°C. Each sensor was tested to determine the impedance response from 1Hz to 5,000Hz. These frequencies correspond to the electrode at the test temperature of 600°C.

Comment on "On the fractal dimension of stream networks"

1990 ◽  
Vol 26 (9) ◽  
pp. 2243-2244 ◽  
Author(s):  
David G. Tarboton
Keyword(s):  
Fractal Dimension ◽  
Stream Networks

Word Complexity Measure

2010 ◽  
Author(s):  
Carol Stoel-Gammon
Keyword(s):  
Complexity Measure
Sign in / Sign up

Export Citation Format

Share Document