A survey of fractal features of Bernoulli percolation

Balankin, Alexander S.

doi:10.1016/j.chaos.2024.115044

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.115044

|View full text |Cite

A survey of fractal features of Bernoulli percolation

Alexander S. Balankin

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 88 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

eFC-Evolving Fuzzy Classifier with Incremental Clustering Algorithm Based on Samples Mean Value

Tavares,

Moita,

Silva

2024

BDCC

View full text Add to dashboard Cite

This paper introduces a new multiclass classifier called the evolving Fuzzy Classifier (eFC). Starting its knowledge base from scratch, the eFC structure evolves based on a clustering algorithm that can add, merge, delete, or update clusters (= rules) simultaneously while providing class predictions. The procedure to add clusters uses the procrastination idea to prevent outliers from affecting the quality of learning. Two pruning mechanisms are used to maintain a concise and compact structure. In the first, redundant clusters are merged based on a similarity measure, and in the second, obsolete and unrepresentative clusters are excluded based on an inactivity strategy. The center of the clusters is adjusted based on the mean value of the attributes. The eFC model was evaluated and compared with state-of-the-art evolving fuzzy systems on 8 randomly selected data streams from the UCI and Kaggle repositories. The experimental results indicate that the eFC outperforms or is at least comparable to alternative state-of-the-art models. Specifically, the eFC achieved an average accuracy of 7% to 37% higher than the competing classifiers. The results and comparisons demonstrate that the eFC is a promising alternative for classification tasks in non-stationary environments, offering good accuracy, a compact structure, low computational cost, and efficient processing time.

show abstract

eFC-Evolving Fuzzy Classifier with Incremental Clustering Algorithm Based on Samples Mean Value

Tavares,

Moita,

Silva

2024

BDCC

View full text Add to dashboard Cite

show abstract

Some Insights into the Sierpiński Triangle Paradox

Martínez-Cruz,

Patiño-Ortiz,

Patiño-Ortiz

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

We realize that a Sierpiński arrowhead curve (SAC) fills a Sierpiński gasket (SG) in the same manner as a Peano curve fills a square. Namely, in the limit of an infinite number of iterations, the fractal SAC remains self-avoiding, such that SAC⊂SG. Therefore, SAC differs from SG in the same sense as the self-avoiding Peano curve PC⊂0,12 differs from the square. In particular, the SG has three-line segments constituting a regular triangle as its border, whereas the border of SAC has the structure of a totally disconnected fat Cantor set. Thus, in contrast to the SG, which has loops at all scales, the SAC is loopless. Consequently, although both patterns have the same similarity dimension D=ln⁡3/ln⁡2, their connectivity dimensions are different. Specifically, the connectivity dimension of the self-avoiding SAC is equal to its topological dimension dlSAC=d=1, whereas the connectivity dimension of the SG is equal to its similarity dimension, that is, dlSG=D. Therefore, the dynamic properties of SG and SAC are also different. Some other noteworthy features of the Sierpiński triangle are also highlighted.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A survey of fractal features of Bernoulli percolation

Cited by 2 publications

References 88 publications

eFC-Evolving Fuzzy Classifier with Incremental Clustering Algorithm Based on Samples Mean Value

eFC-Evolving Fuzzy Classifier with Incremental Clustering Algorithm Based on Samples Mean Value

Some Insights into the Sierpiński Triangle Paradox

Contact Info

Product

Resources

About