This paper investigates the effect of the memory size to fame. A population of individuals of the same memory size is considered. A simple recommendation model is defined based on the memory of the individuals, the social network and the population memory. Recommendation process changes the content of the memory. As the ratio of memory size to population size decreases, a self-organized pattern emerged in who-knows-who graph. Majority of the people become unknown yet a few become very famous. This could be a model for fame and memory.