Swayambhu (also spelled Svayambhu) means Self-manifested or that which is created by its own accord.
Based on details in Bhagavata Purana and Matsya Purana, Narayana or Krishna is said to be the Self-manifested Swayambhu form of Brahman as the first cause of creation. (See Hiranyagarbha).
Several Lingams of Shiva in Hindu temple Garbhagriha have been held sacred as naturally occurring mounds or rocks. Mahakaleshwar Jyotirlinga, the Jyotirlinga at Ujjain, Madhya Pradesh is believed to be one such Swayambhu.
Lord Ganesha appears as a Swayambhu (locals call it: Suyambu) in the "Poyyamozhi" vinayagar temple in Theevanur (15km from Tindivanam - Thiruvannamalai route), a village in Tamil Nadu, India.