Generation of Julia and Mandelbrot Sets via Modified Sp-Iterative Schemes with Image Security Applications
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Abstract
This paper explores modified SP-iterations for both fractal generation and image security applications. We analyze the complex maps ,
, and
for all
and the parameter
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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