Computational technique for lower bound on Two-dimensional Diamond-1 constrained channel capacity is presented in this paper. It is basically an amalgamation of Matrix Fractal Grow Method (MFGM) and a new Matrix Fractal Reduction Method both applicable to state transition matrices of the corresponding constrained channels and Rayleigh Quotient Iteration method. Also other programming tricks are presented which improve its implementation. Estimation of lower bound values on the mentioned capacity is made using it. The results are in good alignment with known exact results, which is a verification of the new method. The method could be generalized for other constraints which are restricted only on one neighbor symbol in 2D constrained channel such as for example Square-1 and Hexagonal-1
