scholarly journals Construction and box dimension of recurrent fractal interpolation surfaces

2021 ◽  
Author(s):  
Zhen Liang ◽  
Huo-Jun Ruan
Keyword(s):  
Box Dimension ◽  
Fractal Interpolation

EXISTENCE AND BOX DIMENSION OF GENERAL RECURRENT FRACTAL INTERPOLATION FUNCTIONS

2020 ◽  
pp. 1-13
Author(s):  
HUO-JUN RUAN ◽  
JIAN-CI XIAO ◽  
BING YANG
Keyword(s):  
Iterated Function System ◽  
General Setting ◽  
Iterated Function Systems ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Iterated Function ◽  
Recurrent System ◽  
Definition Of ◽  
Interpolation Functions

Abstract The notion of recurrent fractal interpolation functions (RFIFs) was introduced by Barnsley et al. [‘Recurrent iterated function systems’, Constr. Approx.5 (1989), 362–378]. Roughly speaking, the graph of an RFIF is the invariant set of a recurrent iterated function system on $\mathbb {R}^2$ . We generalise the definition of RFIFs so that iterated functions in the recurrent system need not be contractive with respect to the first variable. We obtain the box dimensions of all self-affine RFIFs in this general setting.

scholarly journals Bilinear fractal interpolation and box dimension

2015 ◽  
Vol 192 ◽  
pp. 362-378 ◽  
Author(s):  
Michael F. Barnsley ◽  
Peter R. Massopust
Keyword(s):  
Box Dimension ◽  
Fractal Interpolation

BOX DIMENSION OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE OF LINEAR FRACTAL INTERPOLATION FUNCTIONS

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950058 ◽  
Author(s):  
WEN LIANG PENG ◽  
KUI YAO ◽  
XIA ZHANG ◽  
JIA YAO
Keyword(s):  
Fractional Derivative ◽  
Linear Relationship ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

This paper mainly explores Weyl–Marchaud fractional derivative of linear fractal interpolation functions (FIFs). We prove that Weyl–Marchaud fractional derivative of a linear FIF is still a linear FIFs. More generally, we get a conclusion that there exists some linear relationship between the order of Weyl–Marchaud fractional derivative and box dimension of linear FIFs.

A TYPE OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR FRACTIONAL CALCULUS

Fractals ◽  
2016 ◽  
Vol 24 (02) ◽  
pp. 1650026 ◽  
Author(s):  
YONG-SHUN LIANG ◽  
QI ZHANG
Keyword(s):  
Fractional Calculus ◽  
Local Structure ◽  
Continuous Functions ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Chebyshev Systems ◽  
Fractal Interpolation Functions ◽  
The Relationship ◽  
Interpolation Functions

Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann–Liouville fractional calculus and Box dimension of FIF has been investigated.

BOX DIMENSION OF A NONLINEAR FRACTAL INTERPOLATION CURVE

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950023 ◽  
Author(s):  
SONG-IL RI
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Monotone Property ◽  
Interpolation Curve ◽  
Function Convex ◽  
Differential Mean Value Theorem ◽  
Box Dimensions

In this paper, we present a delightful method to estimate the lower and upper box dimensions of a special nonlinear fractal interpolation curve. We use Rakotch contractibility and monotone property of function in the estimation of upper box dimension, and we use Rakotch contractibility, noncollinearity of interpolation points, nondecreasing property of function, convex (or concave) property of function and differential mean value theorem in the estimation of lower box dimension. In particular, we propose a well-founded conjecture motivated by our results.

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.

BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES

2018 ◽  
Vol 98 (1) ◽  
pp. 113-121 ◽  
Author(s):  
QING-GE KONG ◽  
HUO-JUN RUAN ◽  
SHENG ZHANG
Keyword(s):  
Box Dimension ◽  
Fractal Interpolation

Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.

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