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This paper introduces an effective image encryption method based on fractals for colored images. Fractals are now widely used in image security due to its randomness property and infinite boundaries. Since images are traversed over the public channel in day-to-day life confidentiality, integrity and authenticity must be pledged for prosperous transmission. This method capsulizes a larger key space and complex behavior to accomplish a productive confusion and diffusion techniques in a fruitful way. Julia set and Mandelbrot set are constructed and active confusion is exerted till the image pixels are altogether disordered and ensuing diffusion with XOR operation. Experimental results show the ability of the proposed system with respect to various statistical measures. [ABSTRACT FROM AUTHOR]

We describe three different exotic topological objects that arise as Julia sets for complex maps, namely, Cantor bouquets, indecomposable continua, and Sierpinski curves. [ABSTRACT FROM AUTHOR]

To improve the efficiency to find the Julia point in Newton chaos iteration methods, by constructing repulsion three-cycle point function and making use of inverse-image iterative methods, a new method to find Julia set point was introduced. A new method to find all solutions based on utilizing sensitive fraetal areas to locate the Julia set point to find all solutions of the nonlinear questions was proposed. The developed technique uses an important feature of fractals to preserve the shape of basins of attraction on infinitely small scales. The numerical examples in planar crank-slide mechanisms show that the method is effective. [ABSTRACT FROM AUTHOR]