© 2018. American Geophysical Union. All Rights Reserved. Stochastic ionospheric structure is characterized by spectral density functions (SDFs), which are formally the average intensity of Fourier transformations of the electron density structure. Structure elongation along magnetic field lines is typically accommodated by constraining contours of constant spatial correlation to field-aligned ellipsoidal surfaces. Structure realizations are generated by imposing the square root of the SDF onto uncorrelated random Fourier modes. The approach has been used successfully for interpreting both in situ and remote propagation diagnostics. However, the only connection to the field-aligned structures generated by the underlying instability mechanism is the correlation scale. This paper introduces a configuration space model that constructs realizations as summations of field-aligned elemental striations with a prescribed scale and peak electron density. We show that by choosing the contributing scales according to a bifurcation rule and imposing a power law intensity scaling, the corresponding SDF closely approximates an inverse power law. Thus, configuration space realizations can be structured to reproduce prescribed or measured SDFs from one-dimensional scans. Stochastic variation comes from an imposed random distribution of striation locations, which are defined by their intercept in a reference slice plane. To conform more directly to physics-based simulations, the striations can be interpreted as voids in the background electron density. The model is designed to support propagation simulations with arbitrary propagation angles relative to the local magnetic field direction. Relations between in situ structure and diagnostic measurements as well as phase screen equivalence can be explored.