We present a dynamic near-regular texture (NRT) tracking algorithm nested in a lattice-based Markov-Random-Field (MRF) model of a 3D spatiotemporal space. One basic observation used in our work is that the lattice structure of a dynamic NRT remains invariant despite its drastic geometry or appearance variations. On the other hand, dynamic NRT imposes special computational challenges to the state of the art tracking algorithms: including highly ambiguous correspondences, occlusions, and drastic illumination and appearance variations. Our tracking algorithm takes advantage of the topological invariant property of the dynamic NRT by combining a global lattice structure that characterizes the topological constraint among multiple textons and an image observation model that handles local geometry and appearance variations. Without any assumptions on the types of motion, camera model or lighting conditions, our tracking algorithm can effectively capture the varying underlying lattice structure of a dynamic NRT in different real world examples, including moving cloth, underwater patterns and marching crowd.