This work finds a special category of 3-state 3-neighborhood cellular automata that produce only multi length cycles and are named as strictly multi length cycle cellular automata. These automata show their efficacy for clustering problem by a comparative study with existing benchmark clustering algorithms on real datasets. In this work, rule min terms (RMTs) play an instrumental role for the following purposes: i) to generate strictly multi length cycle cellular automata, this work figures out that the rules should maintain a minimum proportion of non self-replicating RMTs; ii) a valid set of non self-replicating RMTs ensures the generation of strictly multi length cycle cellular automaton only and iii) the rules of strictly multi length cycle cellular automata maintain different state values for almost all sibling RMTs and equivalent RMTs to generate the optimal number of clusters (cycles) and maintain less intra-cluster distance (close configurations are in same cluster) which are the key properties for clustering. Additionally, this work finds non-strictly multi length cycle cellular automaton which guarantees the generation of at least one multi length cycle with minimum number of non self-replicating RMTs.