FRACTAL INTERPOLATION SURFACES ON RECTANGULAR GRIDS

2015 ◽  
Vol 91 (3) ◽  
pp. 435-446 ◽  
Author(s):  
HUO-JUN RUAN ◽  
QIANG XU
Keyword(s):  
General Framework ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Rectangular Grids

In this paper, we present a general framework to construct fractal interpolation surfaces (FISs) on rectangular grids. Then we introduce bilinear FISs, which can be defined without any restriction on interpolation points and vertical scaling factors.

scholarly journals CONSTRUCTION OF RECURRENT FRACTAL INTERPOLATION SURFACES WITH FUNCTION SCALING FACTORS AND ESTIMATION OF BOX-COUNTING DIMENSION ON RECTANGULAR GRIDS

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550030 ◽  
Author(s):  
CHOL-HUI YUN ◽  
HUI-CHOL CHOI ◽  
HYONG-CHOL O
Keyword(s):  
Iterated Function System ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Bivariate Interpolation ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Iterated Function ◽  
Rectangular Grids ◽  
Bivariate Functions

We consider a construction of recurrent fractal interpolation surfaces (RFISs) with function vertical scaling factors and estimation of their box-counting dimension. A RFIS is an attractor of a recurrent iterated function system (RIFS) which is a graph of bivariate interpolation function. For any given dataset on rectangular grids, we construct general RIFSs with function vertical scaling factors and prove the existence of bivariate functions whose graph are attractors of the above-constructed RIFSs. Finally, we estimate lower and upper bounds for the box-counting dimension of the constructed RFISs.

RECURRENT FRACTAL INTERPOLATION SURFACES ON TRIANGULAR DOMAINS

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950085 ◽  
Author(s):  
ZHEN LIANG ◽  
HUO-JUN RUAN
Keyword(s):  
General Framework ◽  
Vertical Scaling ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Scaling Factors

We present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on triangular domains. Then we introduce affine RFISs, which are easy to be generated while there are no restrictions on interpolation points and vertical scaling factors. We also obtain the box dimension of affine RFISs under certain constraints.

scholarly journals Fractal interpolation surfaces with function vertical scaling factors

2012 ◽  
Vol 25 (11) ◽  
pp. 1896-1900 ◽  
Author(s):  
Zhigang Feng ◽  
Yizhuo Feng ◽  
Zhenyou Yuan
Keyword(s):  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors

NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION CURVES WITH FUNCTION VERTICAL SCALING FACTORS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050096
Author(s):  
JINMYONG KIM ◽  
HAKMYONG MUN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function Systems ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Hidden Variable ◽  
Iterated Function

In this paper, we present a construction of new nonlinear recurrent hidden variable fractal interpolation curves. In order to get new fractal curves, we use Rakotch’s fixed point theorem. We construct recurrent hidden variable iterated function systems with function vertical scaling factors to generate more flexible fractal interpolation curves. We also give an illustrative example to demonstrate the effectiveness of our results.

Nonlinear fractal interpolation curves with function vertical scaling factors

2020 ◽  
Vol 51 (2) ◽  
pp. 483-499
Author(s):  
JinMyong Kim ◽  
HyonJin Kim ◽  
HakMyong Mun
Keyword(s):  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors

NEW NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION SURFACES

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050038
Author(s):  
HYONJIN KIM ◽  
JINMYONG KIM ◽  
HAKMYONG MUN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function Systems ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Fractal Surfaces ◽  
Hidden Variable ◽  
Iterated Function

In this paper, we present the construction of new nonlinear recurrent hidden variable fractal interpolation surfaces (RHVFISs) with function vertical scaling factors. We use Rakotch’s fixed point theorem which is a generalization of Banach’s fixed point theorem to get new nonlinear fractal surfaces. We construct recurrent vector-valued iterated function systems (IFSs) with function vertical scaling factors on rectangular grids and generate flexible and diverse RHVFISs which are attractors of the IFSs. We also give an explicit example to show the effectiveness of obtained results.

Hidden variable bivariate fractal interpolation functions and errors on perturbations of function vertical scaling factors

2019 ◽  
Vol 12 (02) ◽  
pp. 1950021 ◽  
Author(s):  
Chol-Hui Yun ◽  
Mi-Kyong Ri
Keyword(s):  
Iterated Function System ◽  
Scaling Factor ◽  
Function System ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Iterated Function ◽  
Interpolation Functions

In this paper, we present a construction of hidden variable bivariate fractal interpolation functions (HVBFIFs) with function vertical scaling factors and estimate errors of HVBFIFs on perturbation of the function vertical scaling factor. We construct HVBFIFs on the basis of the iterated function system (IFS) with function vertical scaling factors. The perturbation of the function vertical scaling factors in the IFS causes a change in the HVBFIF. An upper estimation of the errors between the original HVBFIF and the perturbed HVBFIF is given.

scholarly journals ANALYTIC PROPERTIES OF HIDDEN VARIABLE BIVARIABLE FRACTAL INTERPOLATION FUNCTIONS WITH FOUR FUNCTION CONTRACTIVITY FACTORS

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950018 ◽  
Author(s):  
CHOL-HUI YUN ◽  
MI-KYONG LI
Keyword(s):  
Experimental Data ◽  
Data Fitting ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Self Similarity ◽  
Scaling Factors ◽  
Small Perturbations ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

In this paper, we present some analytic properties of hidden variable bivariable fractal interpolation functions (HVBFIFs) with four function contractivity factors presented in [C. H. Yun and M. K. Li, Hidden variable bivariate fractal interpolation functions and errors on perturbations of function vertical scaling factors, Asian-Eur. J. Math. (2017), doi:10.1142/s1793557119500219]. Since four contractivity factors of these HVBFIFs are all functions, the construction of these HVBFIFs has more flexibility and diversity in fitting and approximation of complicated surfaces in nature and irregular experimental data with less self-similarity than one whose four contractivity factors are all constants or only one factor is function. The smoothness and stability of HVBFIFs are needed to ensure the applicability of the HVBFIFs in many practical problems such as the simulation of the objects of the nature, data fitting, etc. We first obtain the results related to their smoothness in nine different cases and then prove that the HVBFIFs are stable to the small perturbations of the interpolation points.

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