scholarly journals Fractal approximation of chaos game representations using recurrent iterated function systems

2019 ◽  
Vol 4 (6) ◽  
pp. 1824-1840
Author(s):  
Martin Do Pham ◽  
Keyword(s):  
Iterated Function Systems ◽  
Iterated Function ◽  
Fractal Approximation ◽  
Chaos Game

scholarly journals A study of the international stock market crash and recovery during COVID-19 pandemic using a modified chaos game representation

2020 ◽  
Author(s):  
Aman Gupta ◽  
Cyril Shaju ◽  
Pratibha ◽  
Kamal
Keyword(s):  
Financial Markets ◽  
Iterated Function Systems ◽  
Chaos Game Representation ◽  
Fractal Method ◽  
Stock Market Crash ◽  
Novel Approach ◽  
Iterated Function ◽  
Before And After ◽  
Chaos Game ◽  
Game Representation

Abstract This paper deals with a novel approach to visualize and compare financial markets across the globe using chaos game representation of iterated function systems. We modified a widely used fractal method to study genome sequences and applied it to study the effect of COVID-19 on global financial markets. We investigate the financial market reaction and volatility to the current pandemic by comparing its behavior before and after the onset of COVID-19. Our method clearly demonstrates the imminent bearish and a surprise bullish pattern of the financial markets across the world.

Some Results on Recurrent Fractal Interpolation Function

2020 ◽  
Vol 12 (8) ◽  
pp. 1038-1043
Author(s):  
Wadia Faid Hassan Al-Shameri
Keyword(s):  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Data Set ◽  
Fractal Interpolation Function ◽  
Iterated Function ◽  
Fractal Functions ◽  
Fractal Approximation

Barnsley (Barnsley, M.F., 1986. Fractal functions and interpolation. Constr. Approx., 2, pp.303–329) introduced fractal interpolation function (FIF) whose graph is the attractor of an iterated function system (IFS) for describing the data that have an irregular or self-similar structure. Barnsley et al. (Barnsley, M.F., et al., 1989. Recurrent iterated function systems in fractal approximation. Constr. Approx., 5, pp.3–31) generalized FIF in the form of recurrent fractal interpolation function (RFIF) whose graph is the attractor of a recurrent iterated function system (RIFS) to fit data set which is piece-wise self-affine. The primary aim of the present research is investigating the RFIF approach and using it for fitting the piece-wise self-affine data set in ℜ2.

Addendum and corrigendum to "On the chaos game of iterated function systems"

2020 ◽  
pp. 1
Author(s):  
Pablo G. Barrientos ◽  
Maxwell Fitzsimmons ◽  
Fatemeh H. Ghane ◽  
Dominique Malicet ◽  
Aliasghar Sarizadeh
Keyword(s):  
Iterated Function Systems ◽  
Iterated Function ◽  
Chaos Game

A FRACTAL APPROXIMATION TO PERIODICITY

Fractals ◽  
2006 ◽  
Vol 14 (04) ◽  
pp. 315-325 ◽  
Author(s):  
M. A. NAVASCUÉS
Keyword(s):  
Iterated Function Systems ◽  
Trigonometric Polynomials ◽  
Small Oscillations ◽  
One Dimensional ◽  
Iterated Function ◽  
Fractal Approximation ◽  
The One ◽  
Circular Functions ◽  
Nature And Society ◽  
Analytical Tools

Periodicity is recurrent in nature and society. The problem of the periodicity is faced here with the support of fractal methodology. Some analytical tools for the understanding of the one-dimensional projections of periodic phenomena are proposed. The reconstruction of an unknown periodic sampled variable is approached, assuming a deterministic self-affine nature in its small oscillations. Fractal trigonometric polynomials are defined by means of suitable iterated function systems. These objects are fractal perturbations of the classical circular functions. The coefficients of the system enable the control and modification of the properties of the originals. Additionally, Fourier parameters and approximants for sampled signals are computed and the density of the fractal trigonometric polynomials in the most common spaces of periodic functions is proved.

scholarly journals On the chaos game of iterated function systems

2016 ◽  
Vol 48 (1) ◽  
pp. 1 ◽  
Author(s):  
Pablo G. Barrientos ◽  
Fatemeh H. Ghane ◽  
Dominique Malicet ◽  
Aliasghar Sarizadeh
Keyword(s):  
Iterated Function Systems ◽  
Iterated Function ◽  
Chaos Game

scholarly journals The chaos game on a general iterated function system

2010 ◽  
Vol 31 (4) ◽  
pp. 1073-1079 ◽  
Author(s):  
MICHAEL F. BARNSLEY ◽  
ANDREW VINCE
Keyword(s):  
Iterated Function System ◽  
General Setting ◽  
Iterated Function Systems ◽  
Function System ◽  
Iterated Function ◽  
Chaos Game ◽  
Weaker Conditions

AbstractThe main theorem of this paper establishes conditions under which the ‘chaos game’ algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non-contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.

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