flash across something
1. Lit. [for something bright] to move quickly across something. The telephone number flashed across the television screen too fast for me to copy it down. The spotlight flashed across the audience, blinding me as it went by.
2. Fig. [for an idea or image] to move quickly through one's mind. A solution to the problem suddenly flashed across my mind. Thoughts of food flashed across my mind, and I began to be very hungry.