We introduce and define a theory of the Bstochastic transition matrix other than the Markov
stochastic transition matrix. We also define and explain
the main assumptions and principles essential to its
validity as well as its inherent characteristics. We compare
the characteristics of matrices B and Markov matrix and
show that both matrices can be real or imaginary and that
their chains work in both real and imaginary spaces. In
particular, matrix B has a striking advantage of being easy
to formulate and simple to manage for 2D and 3D
spatiotemporal diffusion problems with any arbitrary
boundary conditions BC and any arbitrary configuration
of source / sink terms such as case of Poisson and Laplace
partial differential equations as well as heat diffusion PDE.
Finally, we propose a modeling of the 16 vertices of the 4D
hypercube in the cartisian space x, y, z, w by a super
symmetrical matrix B of 16 inputs and 16 outputs.