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2. The Cellular Approach

Cellular algorithms in different implementations have proven applicability in a great variety of problems. Best known are cellular automata (CA) which allow for an intrinsic formulation of conservation laws and a large number of degrees of freedom. Therefore they are applied to many fields where exchange between nearest neighbors is a predominant aspect, e.g., cell growth, molecular analysis, crystallography, and semiconductor applications like diffusion problems [55]. Beyond being base for CA, square and cubic cells are the underlying geometry representation for ortho-grid-based finite differences and differential methods, among others used for semiconductor applications like oxidation of silicon and photo-resist exposure simulation [32]. Finally cell-removal methods have already been implemented previously for topography simulation [10].

Before recapitulating the basic implementation of the applied structuring element algorithm and presenting the most recently achieved optimizations let me summarize other existing topography simulation techniques and discuss differences, advantages, and drawbacks of the different approaches.

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