Besides the major incarnations, there have been many other occasions, when He had designed to be born to men of great austerity and tapas, one such incarnation is the Dattatreya form, which he assumed for the sake of Sage Atri.
Worshipped as the Trinity aspect of the almighty, the Lord appeared in this particular form to fulfill the wishes of Atri and Ansuya. Sage Atri is one of the Saptarishis and derives his name from the fact that he had transcended the three gunas of matter (Sattva, Rajan and Tamas) indicating that he is a realised soul.
The pious couple undertook severe penance sustaining themselves only on air without partaking even water, for the sake of progeny. When they prayed to Lord, they were blessed with Dattatreya.
A mythological story pertains to his birth. Once Narada, the sage of gods went to meet gods in Swarg Lok (heaven) but not meeting them, be only met their consorts Savitri, Lakshmi and Parvati. During his visit, Narada felt that they were all proud of their loyalty towards their husbands. Narada, in his smiling faced typical tone said that he had not seen a more loyal wife than Ansuya, the wife of saint Atri. The three wives, out of jealousy coaxed their husbands to make Ansuya, immoral.
The three gods went to Atri's ashram and in disguised forms, sought food in charity from Ansuya. Ansuya requested them to go, have a dip in the Ganges and come back. When the three returned, they put forth a condition that if she stood naked before them, then only they would take food. Ansuya smelt the rat and sought advice from her husband Atri. Atri, of foresight, gave her some water to wash their feet and sprinkle water on them. Ansuya did, as advised. All the three gods turned into small infants, who started suckling her breast and enjoyed themselves in a cradle.
The three goddesses, after long wait, sought advice from Narada who pointed them to Atri's ashram, the three went there and asked Ansuya about their husbands. Ansuya indicated them to a cradle, in which three infants were playing and sucking their fingers. Unable to recognize, the goddesses requested Ansuya to identify them. Ansuya told them that as they had sucked her breast and had been her children, so they must remain with her.
On this a bright illumination, as a composite reslilt of the three gods, appeared and a three headed and six armed Dattatreya appeared. Ansuya sprinkled water given by her husband Atri, and the three gods came into themselves, in original form. Dattatreya gained knowledge from 24 saints, perfect in different virtues.