Let us look for example on the trajectories of 6 photons as they travel through the IGM, until they are absorbed at the center at redshift $z_\mathrm{abs}=10$. The black line in all plots corresponds to a photon traveling in a straight-line. On large scales, all photons appear to travel in straight-lines as their aparent frequency is far away from the Lyman alpha line center. On small scales, the photons appear to do a random walk with a step size that decreases as we zoom-in, this happens as on the smallest scales the frequency of the photons is close to Lyman alpha and the cross-section for interacting with the hydrogen atoms in the IGM becomes very large.
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