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Linear fractal shape interpolation
1997Proceedings of the Graphics Interface 1997 Conference, Kelowna, British Columbia, Canada, 21 - 23 May 1997, 155 ...
Brandon Burch, John Hart
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Estimating fractal dimension with fractal interpolation function models
IEEE Transactions on Medical Imaging, 1997Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS).
Alan I. Penn, Murray H. Loew
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On the integral transform of fractal interpolation functions
Mathematics and Computers in SimulationA Gowrisankar +2 more
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Curve Fitting by Fractal Interpolation
2008Fractal interpolation provides an efficient way to describe data that have an irregular or self-similar structure. Fractal interpolation literature focuses mainly on functions, i.e. on data points linearly ordered with respect to their abscissa. In practice, however, it is often useful to model curves as well as functions using fractal intepolation ...
Polychronis Manousopoulos +2 more
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Interpolative operators: Fractal to multivalued fractal
Chaos, Solitons & Fractals, 2022Prithvi, B. V., Katiyar, S. K.
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Interpolating and orthogonal polynomials on fractals
Constructive Approximation, 1989A set \(F\subset {\mathbb{R}}^ n\) is said to preserve Markov's inequality if for every \(k\in {\mathbb{N}}\) there is a constant c(n,k,F) such that, for all polynomials P of degree \(\leq k\) and all balls \(B(x_ 0,r)\) with \(x_ 0\in F\) and ...
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FRACTAL INTERPOLATION SURFACES ON RECTANGULAR GRIDS
Bulletin of the Australian Mathematical Society, 2015In 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.
Ruan, Huo-Jun, Xu, Qiang
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Fractal Polynomial Interpolation
Zeitschrift für Analysis und ihre Anwendungen, 2005A general procedure to define non-smooth versions of classical approximants by means of fractal interpolation functions is proposed. A complete and explicit description in the frequency domain of the functions constructed is obtained through their exact Fourier transforms.
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Fractal Interpolation Waveforms
Computer Music Journal, 1995Fractal interpolation is a method of generating functions that pass through given points. We describe the method through an example, illustrated in Figures 1-4. Figure 1 shows four points, through which we will pass a function. Figure 2 shows linear interpolation through the four points; this is the first stage in fractal interpolation, and will be ...
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Fractal functions and interpolation
Constructive Approximation, 1986Consider a set of data points \(\{x_ i,y_ i)\in I\times R:i=0,...,N\}\), where \(I=[x_ 0,x_ N]\subseteq R\). The author considers continuous functions f:I\(\to R\) which interpolate the given data, i.e. \(f(x_ i)=y_ i\), and such that there exist a compact subset \(K=I\times [a,b]\subseteq R^ 2\) and continuous functions \(w_ n:K\to K\) such that the ...
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