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Mathematical Modeling of Pascal Triangular Fractal Patterns and Its Practical Application

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Intelligent Human Computer Interaction (IHCI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12615))

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Abstract

This article focuses on the mathematical modeling of triangular fractal patterns and carpet design in textiles, demonstrating the classic and new arithmetic, combinatorial features of the generalized arithmetic triangles of Pascal’s triangle. Binomial, three-term, and other combinatorial numbers constructed based on recurrence relations have been investigated. The software “Pascal’s Triangle” was developed in the C# programming language. A convenient user interface of the program has been developed. Based on the software implementation, arithmetic triangles are constructed from residues in the form of Pascal’s triangle and combinatorial numbers. The developed software can be used in industry, when drawing patterns, for their subsequent stamping on carpets, fabrics, ceramic tiles, etc.

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Authors and Affiliations

  1. Tashkent University of Information Technologies, 100200, Tashkent City, Republic of Uzbekistan

    Sh. A. Anarova

  2. Samarkand Branch of Tashkent University of Information Technologies Named After Muhammad al-Khwarizmi, Tashkent, Uzbekistan

    Z. E. Ibrohimova

  3. Tashkent University of Information Technologies Named After Muhammad al-Khwarizmi, Tashkent, Uzbekistan

    O. M. Narzulloyev & G. A. Qayumova

Authors
  1. Sh. A. Anarova
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  2. Z. E. Ibrohimova
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  3. O. M. Narzulloyev
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  4. G. A. Qayumova
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Corresponding authors

Correspondence to Sh. A. Anarova , Z. E. Ibrohimova , O. M. Narzulloyev or G. A. Qayumova .

Editor information

Editors and Affiliations

  1. Woosong University, Daejeon, Korea (Republic of)

    Madhusudan Singh

  2. Dongseo University, Busan, Korea (Republic of)

    Dae-Ki Kang

  3. Keimyung University, Daegu, Korea (Republic of)

    Jong-Ha Lee

  4. Indian Institute of Information Technoloy, Allahabad, India

    Uma Shanker Tiwary

  5. Hankuk University of Foreign Studies, Yongin, Korea (Republic of)

    Dhananjay Singh

  6. Pukyong National University, Busan, Korea (Republic of)

    Wan-Young Chung

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Anarova, S.A., Ibrohimova, Z.E., Narzulloyev, O.M., Qayumova, G.A. (2021). Mathematical Modeling of Pascal Triangular Fractal Patterns and Its Practical Application. In: Singh, M., Kang, DK., Lee, JH., Tiwary, U.S., Singh, D., Chung, WY. (eds) Intelligent Human Computer Interaction. IHCI 2020. Lecture Notes in Computer Science(), vol 12615. Springer, Cham. https://doi.org/10.1007/978-3-030-68449-5_39

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  • DOI: https://doi.org/10.1007/978-3-030-68449-5_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68448-8

  • Online ISBN: 978-3-030-68449-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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