Dreams about being chased often symbolize feelings of anxiety or avoidance in waking life. The celebrity look-alike could represent a part of yourself that you admire or aspire to, or it may reflect societal pressures and expectations you feel. The progression from hiding to confronting your pursuer suggests personal growth and a willingness to face your fears.

The colors you mentioned—white, black, and grey—can also hold significance. White often represents purity or new beginnings, black can symbolize the unknown or fear, and grey may indicate uncertainty or a transition phase. This color palette might reflect your emotional state or the complexity of the situation you’re dealing with.

Consider what aspects of your life you might be avoiding and how you can confront those challenges. The recurring nature of the dream suggests that this is an important issue for you. Reflect on what the celebrity represents for you and how that relates to your own self-image and aspirations. Embrace the courage you've shown in moving from hiding to confronting; it’s a positive sign of your inner strength and growth.