Arnold Transformation in MATLAB with Inverse Transformation and Period Calculation

This document presents a comprehensive implementation of Arnold's transformation using MATLAB. Arnold transformation is a chaotic mapping technique commonly employed for digital image scrambling and descrambling operations. The implementation covers both forward transformation (image scrambling) and inverse transformation (image recovery) algorithms using matrix operations. The core transformation utilizes a 2x2 transformation matrix applied iteratively to pixel coordinates, with modular arithmetic to maintain image boundaries. For period calculation, the algorithm tracks transformation iterations until the image returns to its original state, implementing cycle detection through coordinate comparison. Key MATLAB functions employed include matrix multiplication for coordinate transformation, mod() for boundary handling, and iterative loops for period analysis. The implementation demonstrates how to calculate the transformation period - the number of iterations required for an image to revert to its initial configuration, which is crucial for understanding chaotic system behavior in image encryption applications. By studying this material, you will gain practical knowledge of Arnold transformation mechanics, learn to implement both scrambling and descrambling operations in MATLAB, and understand period computation methods for various image dimensions in digital image security applications.