# Novel method of fractal approximation

@article{Igudesman2012NovelMO, title={Novel method of fractal approximation}, author={K. Igudesman and G. Shabernev}, journal={Lobachevskii Journal of Mathematics}, year={2012}, volume={34}, pages={125-132} }

We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of approximation, which are based on a similar optimization scheme, on the various types of data: polynomial function, DNA primary sequence, price graph and graph of random walking.

#### 6 Citations

Novel Approach to Calculation of Box Dimension of Fractal Functions

- Mathematics
- 2014

We introduce new method of calculation of box dimension of fractal functions’ graphs, which are based on fractal interpolation functions. Provide a comparison of the eectiveness of the traditional… Expand

New Approach to Fractal Approximation of Vector-Functions

- Mathematics
- 2015

This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal… Expand

Explicitly defined fractal interpolation functions with variable parameters

- Mathematics
- 2015

Abstract We construct an explicit formula for the fractal interpolation function associated to an IFS with variable parameters. The solution is given in terms of the base p representation of numbers.… Expand

Fractal approximation of vector functions

- Mathematics
- 2013

We present a new approach to the approximation of continuous vector-valued functions by fractal interpolative vector-valued ones and find optimal values of their parameters. We illustrate the… Expand

Bilinear fractal interpolation and box dimension

- Computer Science, Mathematics
- J. Approx. Theory
- 2015

In the context of general iterated function systems (IFSs), bilinear fractal interpolants are introduced as the fixed points of certain Read-Bajraktarevic operators by exhibiting a generalized "taxi-cab" metric and presenting an explicit formula for the box-counting dimension of the graph of a bilin EAR interpolant in the case of equally spaced data points. Expand

Self-Similar Models and How to Find Them: A Moment Theory Approach

- Mathematics
- 2018

Self-similar modelling aims to capture how an object relates to itself, and can be done through fractal geometry. Creating a fractal that looks like a natural object is easy, finding a fractal that… Expand

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