Probabilistic tractography has emerged as an alternative to classical deterministic methods to overcome their lack of connectivity information between different brain regions. However, it relies on statistical sampling, which is computationally taxing. In this study, a well-known, random walk based stochastic tractography method is discretized by limiting the set of directions that a sampling particle can follow. This sets up to a framework based on a Markov chain that can accommodate all the desirable features of stochastic tractography, principally trajectory regularization through particle deflection. The system produces results that are comparable to those by the stochastic algorithm it is based on (ρ = 0.79), though 60 times faster.