The correct option is Badami.
Explanation
The synthesis of rock-cut architecture and mural painting reached its zenith at Ajanta (primarily under the Vakatakas and Guptas). This tradition of decorating excavated caves with extensive wall paintings did not cease with Ajanta but was carried forward into the Deccan by the early Chalukyas of Badami in the 6th century CE.Detailed Analysis:
- Badami Badami: The Badami Caves in Karnataka represent the continuation of the mural tradition seen at Ajanta. Specifically, Cave No. 4 (dedicated to Vishnu) contains surviving fragments of paintings, such as the panel of "Indra and his retinue" and the "Queen and attendants." These murals, patronized by the Chalukya king Mangalesha (circa 578-598 CE), exhibit stylistic affinities with Ajanta in terms of line, modeling, and color application, making Badami the immediate successor in the tradition of painted rock-cut caves.
- Hampi Hampi: Hampi serves as the capital of the Vijayanagara Empire (14th-16th century CE). While the Virupaksha Temple at Hampi contains ceiling paintings, these belong to a much later period and are associated with structural temple architecture, not the ancient rock-cut cave tradition.
- Thanjavur Thanjavur: Thanjavur is renowned for the Brihadeeswara Temple, a structural masterpiece of the Chola period (11th century CE). While it houses significant Chola frescoes within the circumambulatory passage of the vimana, it does not represent the cave excavation tradition.
- Lepakshi Lepakshi: The Veerabhadra Temple at Lepakshi (16th century CE) is famous for its Vijayanagara-style murals. Like Hampi and Thanjavur, it is a structural temple complex and is chronologically distant from the Ajanta-Badami era.
Key Takeaway:
Badami Cave No. 4 provides the earliest surviving evidence of Brahmanical wall paintings in India, marking the direct continuity of the Ajanta tradition of simultaneously sculpting and painting in cave excavations.