Novel method of fractal approximation

TL;DR

This paper presents a new optimization method for affine iterated function systems to improve fractal approximation, comparing its effectiveness across different data types like polynomials, DNA sequences, and price graphs.

Contribution

It introduces a novel optimization approach for affine IFS parameters and compares fractal and quadratic approximation methods on diverse datasets.

Findings

Fractal approximation can be effectively optimized using the proposed method.

Fractal and quadratic approximations show different effectiveness depending on data type.

The method demonstrates versatility across polynomial, biological, financial, and stochastic data.

Abstract

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.