The Fathers explored this mystery that no human language can express. There is no being in nature that is one essence in three distinct hypostases. When we use any analogy for the mystery of the Holy Trinity, we must acknowledge up front that it cannot be anything other than imperfect, capturing some aspects but not others, in order that our minds may be able to comprehend. We cannot approach this mystery without the divine grace that grants us to partake of the Holy Trinity; the communion with the Father, by His Son, through the Holy Spirit. Here are a few patristic analogies of the Holy Trinity:
Human beings are created in the image of God (Gen. 1:27; 2:5). A person exists as a rational and living soul. The soul is one, yet its reasoning mind and its life are distinct from each other. Nonetheless, these three entities — soul, mind, and life — cannot be separated from each other.
God promised to protect His Church, saying, “And I will be a wall of fire around her, and I will be glory in her midst” (Zech. 2:5). Fire has three intrinsic properties that resemble the Hypostases: flames; and the light and heat that are emitted from them ; but they are not hypostases, because no one of them fills the others. Through the light and the heat we can come to know the fire.
The sun exists as a star, and it emits rays of light and radiates heat; yet it is one sun. The star itself is called the sun, its rays are called the sun, and its heat is called the sun as well.
God is like an apple, as it is said: “Like an apple tree among the trees of the woods, so is my beloved among the sons” (Song 2:3). The apple has three properties: the physical material we eat; its taste; and its smell , and we can know the apple from its taste or smell.