In this paper, we present a data-driven approach for automatically generating South Indian rhythmic patterns. The method uses a corpus of Carnatic percussion compositions and grooves performed in adi tala - a uniform eight-beat cycle. To model the rhythmic structure and the generation process of phrasings that fit within the tala cycles, we use a set of arithmetic partitions that model the strategies used by professional Carnatic percussionists in their performance. Each partition consists of combinations of stroke sequences. This modeling approach has been validated in terms of the groupings used in this music idiom by direct discussions with Carnatic music experts. Two approaches were used for grouping the sequences of strokes into meaningful rhythmic patterns. The first is based on a well-formed dictionary of prerecorded phrase variations of stroke groupings and the second one on a segmentation algorithm that works by comparing the distance of adjacent strokes. The sequences of strokes from both approaches were later analyzed and clustered by similarity. The results from these analyses are discussed and used to improve existing generative approaches for modelling this particular genre by emulating Carnatic-style percussive sequences and creating rhythmic grooves. The creation of these tools can be used by musicians and artists for creative purposes in their performance and also in music education as a means of actively enculturing lay people into this musical style.