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A stochastic model of an experimentally measured unit cell structure is computed using the multi-scale textile software WiseTex. The statistical characteristics of a sample, derived in prior work, are used to calibrate the recently proposed Markov Chain algorithm for textile fabrics. The generated variable tow reinforcements are transformed in the WiseTex format that is compatible with tools for micromechanical analysis and permeability simulation. The application is a seven ply polymer textile composite, with each ply consisting of a twill 2/2 woven carbon fabric in an epoxy matrix. The developed model possesses random tow centroid paths with nominal cross-sectional properties.