Final answer:
Batik first flourished in the Indonesian islands of Java and Sumatra, where the technique has been an integral part of the culture and economy.
Step-by-step explanation:
The states of Java and Sumatra are where batik first flourished.
Batik is a fabric dyeing technique that uses wax to create intricate designs on cloth. Originating in Indonesia, batik has a rich history tied to the culture and economies of various Indonesian islands. When the Dutch colonized Indonesia in the 1700s, they were impressed by the batik techniques and sought to mass-produce similar textiles using block printing. This eventually spread to Africa where Dutch wax cloth became a significant part of African textile culture.
Indonesian islands such as Java Island, Sumatra, and others like Kalimantan and Madura have been influential in the development of batik. West Java, Jakarta, and Banten are specific regions within these islands where batik has historically been an integral part of the culture and trade. Java, in particular, is renowned for its batik tradition, which has become recognized worldwide.