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Dynamic texture describes the images sequence that continuously demonstrates movement of pixel's intensity change patterns in time. Two motion features, namely average radius and motion coherence index are extracted to find the different characteristics of fire and smoke. Since, the average radius of motion vectors describes the rapid of intensity change, whilst the motion coherence index has been developed to assess the coherent motion of intensity change. We propose a cutting-edge periodic series analysis to characterize fire and smoke dynamic textures. Our experimental results demonstrate the periodic motion pattern of fire and smoke. Besides, the periodicity index calculated by our proposed method is efficiently able to characterize fire and smoke dynamic textures, higher efficiency than calculated by traditional approach.