This chapter investigates which agent-based mechanisms can or cannot generate near repeat patterns in serial victimizations of targets located in an abstract geographical space. Crime pattern theory suggests that offenders have an awareness space within which they will make a choice of targets. We propose dynamics on how awareness space changes over time, first as a function of previous awareness only (DAS-model), then as a function of previous target choices (CAS-model). Congruent with the near repeat literature, we look into the boost mechanism of temporary increase of attraction values of targets nearby previously victimized targets (CBA-model). We also look into cases where an offender victimizes more targets at nearly the same time (SPATE). We introduce a new yardstick, the Knox Sloping-down Index ξ, to compare the strength of near repeat patterns. Results show that DAS and CAS are not able to generate near repeat patterns, but CBA and SPATE are, both alone and more so in combination.