In this paper we explore a method for automatically generating Carnatic style rhythmic. The method uses a set of annotated Carnatic percussion performances to generate new rhythmic patterns. The excerpts are short percussion solo performances in ādi tāla (8 beat-cycle), performed in three different tempi (slow/moderate/fast). All excerpts were manually annotated with beats, downbeats and strokes in three different registers - Lo-Mid-Hi. N-gram analysis and Markov chains are used to model the rhythmic structure of the music and determine the progression of the generated rhythmic patterns. The generated compositions are evaluated by a Carnatic music percussionist through a questionnaire and the overall evaluation process is discussed. Results show that the system can successfully compose Carnatic style rhythmic performances and generate new patterns based on the original compositions.