Generation of Julia and Mandelbrot Sets via Modified Sp-Iterative Schemes with Image Security Applications

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Published: Jun 30, 2026
DOI: https://doi.org/10.70730/sta.v31i2.263926
Keywords:
Escape criteria Fractals Image encryption Image security Modified SPiterative method

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Nabaraj Adhikari
Central Department of Mathematics, Institute of Science and Technology Tribhuvan University, Kathmandu 44613, Nepal

Abstract

This paper explores modified SP-iterations for both fractal generation and image security applications. We analyze the complex maps equation,  equation, and equation for all equationand the parameter equation establishing an escape criterion that enables generation of diverse Julia and Mandelbrot sets. Algorithm implementation demonstrates parameterdependent variations in fractal patterns and symmetry. Using these chaotic properties, we develop an integrated encryption-enhancement system combining modified SP-iteration based security with median filtering. The method achieves strong encryption (NPCR > 99.6%, UACI > 33.4%) and high-quality reconstruction (PSNR up to 45.73 dB, SSIM > 0.99). This work bridges fractal mathematics with practical image processing, demonstrating how complex iterations can simultaneously produce aesthetic fractals and secure digital images.

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How to Cite
Nabaraj Adhikari. (2026). Generation of Julia and Mandelbrot Sets via Modified Sp-Iterative Schemes with Image Security Applications. Science & Technology Asia, 31(2), 45–66. https://doi.org/10.70730/sta.v31i2.263926
Issue
Vol.31 No.2 (April-June 2026)
Section
Physical sciences
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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