The Avatamsaka Sutra influenced the Huayan school of Buddhism, which in turn influenced Cha'an:"Interpenetration" of all phenomena: the ultimate principle of all things is emptiness; every
individual thing fully manifests the ultimate principle of everything else. Developed in Huayan
school. Indra's Net.
http://www2.kenyon.edu/Depts/Religion/F ... na-360.pdf
When Chinese Pure Land Buddhism became fused with Ch'an, it incorporated the Huayan teaching of the interpenetration of principle and phenomena:Chinese Chán was profoundly influenced by it, though Chán also defined itself by distinguishing itself from Huayan. Tsung-mi, the Fifth Patriarch of the Hua-yen school, also occupies a prominent position in the history of Chán. During the Song, the Hua-yen metaphysics were completely assimilated by the Chán-school.
We can also go back further into the history of Pure Land Buddhism, before the influence of Chinese Ch'an, to see the above teaching.Master Ou-i also reflects upon Amitabha's Land of Ultimate Bliss from the perspective of Hua-yen Buddhism, where the interpenetration of infinite arrays of worlds is the basic medium of the enlightening being's perception. Master Ou-i stresses this in his comments on the passage in the sutra describing the inhabitants of Amitabha's Pure Land returning from their regular journeys to other worlds...
Master Ou-i comments: "This passage shows that in the Pure Land every sound, every sense-object, every moment, and even every step and every snap of the fingers, interpenetrates without obstruction the Three Jewels of all the worlds of the ten directions. It also shows that in our mundane world the defilements and obstructions are so serious that our world is separated off from the Land of Ultimate Bliss, even though it is not really separated from it...
The word "Buddha" is also used to refer to the inherent potential for enlightened perception that all people share. According to Great Vehicle Buddhism, we all have "Buddha-nature", and the one great mission of all forms of Buddhism is to bring this to light, to make us aware of our Buddha-nature, and enable us to function by means of it in our daily lives. In this context, remembering Buddha, Buddha-remembrance, means remembering our own true nature, the capacity for lucid wisdom and selfless compassion that is our birthright. By becoming mindful of Buddha (i.e. reciting the Buddha-name), we are just regaining our real identity.
http://www.ymba.org/books/mind-seal-bud ... abha-sutra
The earliest scriptural mention of Amitabha Buddha is in Pratyutpanna Samādhi Sūtra, whose intent is to experience Amitabha and other Buddhas as one's true nature:
https://en.wikipedia.org/wiki/Pratyutpa ... S%C5%ABtra
Also, the teaching of the interpenetration of Amitabha Buddha and ourselves can be found in the Contemplation Sutra, one of the three canonical Pure Land sutras:
Whether Amitabha Buddha is a literal flesh and blood Buddha from ten kalpas ago, or is symbolic of Dharma-body, the underlying idea is the name: In reciting the name of Amida Buddha, we are calling the name of our true nature, awakening the Buddha within. This is due to the interpenetration of principle and phenomena.17. 'When you have perceived this, you should next perceive Buddha himself. Do you ask how? Every Buddha Tathagata is one whose spiritual body is the principle of nature (Darmadhatu-kaya), so that he may enter into the mind of any beings. Consequently, when you have perceived Buddha, it is indeed that mind of yours that possesses those thirty-two signs of perfection and eighty minor marks of excellence which you see in a Buddha. In conclusion, it is your mind that becomes Buddha, nay, it is your mind. that is indeed Buddha. The ocean of true and universal knowledge of all the Buddhas derives its source from one's own mind and thought. Therefore you should apply your thought with an undivided attention to a careful meditation on that Buddha Tathagata, Arhat, the Holy and Fully Enlightened One.