This study presents experimental observations of chaotic thermoacoustic oscillations induced in a looped tube with respect to both temporal and spatial dimensions and compares them with those in a resonance tube system. The wave propagation directions observed in thermoacoustic systems showing periodic behaviors are confirmed in the chaotic case, from cold to hot sides in the stack in a looped system, and with reflections at the ends of a resonance tube system. Although both systems are similar in their route to chaos and correlation dimensions of the chaotic attractor, a recurrence visualization method reveals differences in the distribution of temporal patterns resulting from the mode competition between the natural frequencies of the systems.