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The collapsing dynamics of a trapped Bose-Einstein condensate (BEC) with attractive interaction are revealed to exhibit two previously unknown phenomena. During the collapse, BEC undergoes a series of rapid implosions that occur {\it intermittently} within a very small region. When the sign of the interaction is suddenly switched from repulsive to attractive, e.g., by the Feshbach resonance, density fluctuations grow to form various patterns such as a shell structure.

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