Fractal Dimension of Coalescence Hidden-Variable Fractal Interpolation Surface

Prasad, Srijanani Anurag; Kapoor, G. P.

doi:10.1142/s0218348x11005336

Cited by 8 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The graph of the of the function f α may have non-integer fractal dimensions [5,6]. For results on the fractal dimensions of different fractal functions, interested reader may see [4,[7][8][9][10][11][12][13][14] and references therein. In [15], the authors introduces the novel notion of dimension preserving approximation for continuous functions defined on [0, 1] and initiates the study of it.…”

Section: Introductionmentioning

confidence: 99%

New fractal functions on the sphere

Akhtar

Prasad

Navascués

et al. 2021

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

In this article, a family of continuous functions on the unit sphere S ⊆ R 3 is considered as a generalization of spherical harmonics. The family is fractalized using a linear and bounded operator of functions on the sphere. Particular values of the scale vector in the iterated function system (IFS) may yield classical functions system on the sphere. We have shown that for different values of the scale vector in the IFS, Bessel sequences, frames, and Riesz bases can be established for the space L 2 (S) of square integrable functions on the sphere.

show abstract

Section: Introductionmentioning

confidence: 99%

New fractal functions on the sphere

Akhtar

Prasad

Navascués

et al. 2021

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

show abstract

“…In 1986, M. F. Barnsley [1] introduced a concept of FIF to model better natural phenomena which are irregular and complicated and the FIFs have been widely studied ever since in many papers. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][17][18][19][20][21][22] In general, to get the FIF, we construct an iterated function system (IFS) on the basis of a given data set and then define a Read-Bajraktarevic operator on some space of continuous functions. A fixed point of the operator is an interpolation function of the data set and its graph is an attractor of the constructed IFS.…”

Section: Introductionmentioning

confidence: 99%

“…K. B. Chand and G. P. Kapoor [5] studied a coalescence hidden variable fractal interpolation function using the IFS with free parameters and constrained free parameters. In many articles, authors have studied smoothness [5, 12 and 22], stability [6, 13, 21 and 22] and fractal dimension [5,15] of HVFIFs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors

Yun¹,

Ri²

2020

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

We estimate the bounds of box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present analytic properties of HVFIFs which are constructed to ensure more flexibility and diversity in modeling natural phenomena. Firstly, we construct the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the lower and upper bounds of box-counting dimension of the HVFIFs. Finally, in the similar way, we get the lower and upper bounds of box-counting dimension of HVBFIFs constructed in [21].

show abstract

“…The most important fact is that under DLCA, the D f value is around 1.8 for rigid non-coalescence particles and equals 3.0 for soft complete coalescence systems [6,7,18]. Thus, if we perform the aggregation under DLCA conditions, each D f value between the two extremes, 1.8 and 3.0, represents different extent of the coalescence.…”

Section: Introductionmentioning

confidence: 99%

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

Wei

Xia

et al. 2012

Colloid Polym Sci

View full text Add to dashboard Cite

The fractal dimension (D f ) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reactionlimited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.

show abstract

Fractal Dimension of Coalescence Hidden-Variable Fractal Interpolation Surface

Cited by 8 publications

References 9 publications

New fractal functions on the sphere

New fractal functions on the sphere

Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

Contact Info

Product

Resources

About