Both networks with hexagonal topology in 2D and networks with dodecahedral topology in 3D have a lot of properties, which should generate new results in the case of diffusion simulation with chemical reaction and other applications. These topologies also enables advanced non-linear image processing (smoothing, enhancement, reconstruction, texture analysis) and very fast linear image processing using fast Fourier transform. A design of data structures and algorithms for real system simulation is the main subject of research together with following implementation with easy formulation of individual mathematical model. Knowledge of numerical methods for partial differential equation solving and ability of efficient implementation in the Matlab environment are required.
References:
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- Kukal, J., Van Tran, Q., & Benes, M. (2019). Discovery of rare event testing for stochastic simulations of diffusion processes. Physica A: Statistical Mechanics and its Applications, 525, 50-63.
- Pitas, I., & Venetsanopoulos, A. (1986). Nonlinear mean filters in image processing. IEEE transactions on acoustics, speech, and signal processing, 34(3), 573-584.
- Sicuranza, G. (2000). Nonlinear image processing. Elsevier.
- Middleton, L., & Sivaswamy, J. (2005). Hexagonal image processing: A practical approach. Springer Science & Business Media.
