Complex Chaotic Attractor via Fractal Transformation

Dai, Shengqiu; Sun, Kehui; He, Shaobo; Ai, Wei

doi:10.3390/e21111115

Cited by 22 publications

(9 citation statements)

References 42 publications

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“…However, the dynamic behaviors and hardware implementation of the separated attractors were not given to prove the excellent performance of this method. Dai et al [22] introduced the ternary fractal method based on the binary fractal algorithm by extending the number of input sequences to three from two, implying that the attractors can be exhibited in three-dimensional space. Although the paper presents the dynamics analysis and hardware implementation of multi-scroll attractors, more complex attractors such as separated attractors, and nested attractors were not given.…”

Section: Introductionmentioning

confidence: 99%

Multi-ring julia fractal chaotic systems with separated scrolls and nested scrolls

Yan,

Yang,

Duan

et al. 2023

Phys. Scr.

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Chaos and fractals are two branches of nonlinear science. However, few scholars have combined chaos and fractals for generating chaotic attractors with different topologies. The main goal of this paper is to combine fractals and chaos to generate separated multi-scroll attractors and nested multi-scroll attractors, as well as to compensate for the lack of randomness and complexity of general chaotic systems. Combining chaotic attractors with two different fractal processes, a class of multiscroll chaotic attractors with different behaviors are generated, including multi-ring attractors, separated multi-ring attractors, and nested multi-ring attractors.The experiments of spectral entropy (SE) complexity indicates that the proposed multi-ring fractal systems have higher complexity than other chaotic systems. Furthermore, from the perspective of engineering applications, the random performance of one of the multi-ring fractal systems is tested by the NIST test suite. The results demonstrate that the multi-ring fractal system has promising randomness and is well suited for-image encryption applications. Finally, the numerical simulation results are well illustrated by the micro-controller unit (MCU) hardware experiments, which reveal the feasibility of the designed multi-ring attractors, separated multi-ring attractors, and nested attractors.a

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Section: Introductionmentioning

confidence: 99%

Multi-ring julia fractal chaotic systems with separated scrolls and nested scrolls

Yan,

Yang,

Duan

et al. 2023

Phys. Scr.

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“…We can apply the GFD method to compare the Sobel, Prewitt and Robert edge detection method’s complexity of the various COVID-19 patient’s images. The qualitative measure is useful during image processing, distortion caused by noise, blurring, sounds and abstract artifacts will impair image quality [ 11 ]–[ 18 ]. When doing other qualities with distorted images, the value of the uncompressed image is useful.…”

Section: Introductionmentioning

confidence: 99%

Generalized fractal dimensions based comparison analysis of edge detection methods in CT images for estimating the infection of COVID-19 disease

Thangaraj

Easwaramoorthy

2022

Eur. Phys. J. Spec. Top.

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The coronavirus, also known as COVID-19, has become highly contagious and has been associated with one of the world’s deadliest diseases. It also has direct effects on human lungs, causing significant damage. CT-scans are commonly employed in such circumstances to promptly evaluate, detect, and treat COVID-19 patients. Without any filtering, CT-scan images are more difficult to identify the damaged parts of the lungs and determine the severity of various diseases. In this paper, we use the multifractal theory to evaluate COVID-19 patient’s CT-scan images to analyze the complexity of the various patient’s original, filtered, and edge detected CT-scan images. To precisely characterize the severity of the disease, the original, noisy and denoised images are compared. Furthermore, the edge detection and filtered methods called Robert, Prewitt, and Sobel are applied to analyze the various patient’s COVID-19 CT-scan images and examined by the multifractal measure in the proposed technique. All of the images are converted, filtered and edge detected using Robert, Prewitt, and Sobel edge detection algorithms, and compared by the Generalized Fractal Dimensions are compared. For the CT-scan images of COVID-19 patients, the various Qualitative Measures are also computed exactly for the filtered and edge detected images by Robert, Prewitt, and Sobel schemes. It is observed that Sobel method is performed well for classifying the COIVD-19 patients’ CT-scans used in this research study, when compared to other algorithms. Since the image complexity of the Sobel method is very high for all the images and then more complexity of the images contains more clarity to confirm the COVID-19 images. Finally, the proposed method is supported by ANOVA test and box plots, and the same type of classification in experimental images is explored statistically.

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“…The image’s non-uniformity or inhomogeneity cannot be described by a single-dimensional measure. This dimensional scale is insufficient to classify the experimental image’s randomness or inconsistency [ 8 – 11 ]. A Multifractal is an inhomogeneous set that is defined by the Generalized Fractal Dimensions (GFD) or Renyi Fractal Dimensions.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis on age-based discrimination in X-ray images for sensing the severity of COVID-19 disease

Thangaraj

Easwaramoorthy

et al. 2022

Eur. Phys. J. Spec. Top.

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Complex Chaotic Attractor via Fractal Transformation

Cited by 22 publications

References 42 publications

Multi-ring julia fractal chaotic systems with separated scrolls and nested scrolls

Multi-ring julia fractal chaotic systems with separated scrolls and nested scrolls

Generalized fractal dimensions based comparison analysis of edge detection methods in CT images for estimating the infection of COVID-19 disease

Multifractal analysis on age-based discrimination in X-ray images for sensing the severity of COVID-19 disease

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