Burst detection over data streams has been attracting more and more attention from academic and industry communities due to its broad potential applications in venture analysis, network monitoring, trend analysis and so on. This paper aims at detecting bursts of both monotonic and non-monotonic aggregates over multiple windows in data streams. A burst detection algorithm through building monotonic search space based on fractal technique is proposed. First, the piecewise fractal model on data stream is introduced, and then based on this model the algorithm for detecting bursts is presented. The proposed algorithm can decrease the time complexity from O(m) to O(logm), where m is the number of sliding windows being detected. Two novel piecewise fractal models can model the self-similarity and compress data streams with high accuracy. Theoretical analysis and experimental results show that this algorithm can achieve a higher precision with less space and time complexity as compared with the existing methods, and it could be concluded that the proposed algorithm is suitable for burst detection over data streams.