The Chaos Game: How Randomness Creates Deterministic Shapes

1992 ◽  
pp. 297-352
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Chaos Game

scholarly journals Proton Exchange Membrane Fuel Cells Modeling Using Chaos Game Optimization Technique

2021 ◽  
Vol 13 (14) ◽  
pp. 7911
Author(s):  
Ibrahim Alsaidan ◽  
Mohamed A. M. Shaheen ◽  
Hany M. Hasanien ◽  
Muhannad Alaraj ◽  
Abrar S. Alnafisah
Keyword(s):  
Fuel Cell ◽  
Objective Function ◽  
Proton Exchange Membrane ◽  
Optimization Technique ◽  
Proton Exchange ◽  
Simulation Performance ◽  
Terminal Voltage ◽  
Chaos Game ◽  
Simulation Results ◽  
Exchange Membrane

For the precise simulation performance, the accuracy of fuel cell modeling is important. Therefore, this paper presents a developed optimization method called Chaos Game Optimization Algorithm (CGO). The developed method provides the ability to accurately model the proton exchange membrane fuel cell (PEMFC). The accuracy of the model is tested by comparing the simulation results with the practical measurements of several standard PEMFCs such as Ballard Mark V, AVISTA SR-12.5 kW, and 6 kW of the Nedstack PS6 stacks. The complexity of the studied problem stems from the nonlinearity of the PEMFC polarization curve that leads to a nonlinear optimization problem, which must be solved to determine the seven PEMFC design variables. The objective function is formulated mathematically as the total error squared between the laboratory measured terminal voltage of PEMFC and the estimated terminal voltage yields from the simulation results using the developed model. The CGO is used to find the best way to fulfill the preset requirements of the objective function. The results of the simulation are tested under different temperature and pressure conditions. Moreover, the results of the proposed CGO simulations are compared with alternative optimization methods showing higher accuracy.

scholarly journals Chaos game for IFSs on topological spaces

2016 ◽  
Vol 435 (2) ◽  
pp. 1458-1466 ◽  
Author(s):  
Michael F. Barnsley ◽  
Krzysztof Leśniak ◽  
Miroslav Rypka
Keyword(s):  
Topological Spaces ◽  
Chaos Game

Test on the Structure of Biological Sequences via Chaos Game Representation

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Peggy Cénac
Keyword(s):  
Markov Chain ◽  
Statistical Tests ◽  
Biological Sequences ◽  
Chaos Game Representation ◽  
New Family ◽  
Chaos Game ◽  
Tests For Independence ◽  
Game Representation

In this paper biological sequences are modelled by stationary ergodic sequences. A new family of statistical tests to characterize the randomness of the inputs is proposed and analyzed. Tests for independence and for the determination of the appropriate order of a Markov chain are constructed with the Chaos Game Representation (CGR), and applied to several genomes.

scholarly journals APPLICATION OF CHAOS GAME REPRESENTATION TO NONLINEAR TIME SERIES ANALYSIS

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 27-35 ◽  
Author(s):  
TOMOYA SUZUKI ◽  
TOHRU IKEGUCHI ◽  
MASUO SUZUKI
Keyword(s):  
Time Series ◽  
Real Time ◽  
Dna Sequences ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Conditional Probabilities ◽  
Fractal Structures ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

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