We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.