Trinity illustrations tend to breakdown. The water one illustrates modalism not historic, orthodox trinitarianism. The egg one doesn't resonate with me. I found one that does, however. James Smith came up with it. It is the illustration of music, or a song. For a song to exist, it must be composed, produced, and heard. In other words, it needs a source, a score, and a sound.
Think about the trinity. The Father is the Source. He is the ground and originator of creation and us. The Son is the Score. He is the word, divine music written and revealed. The Spirit is the Sound. He is the love and power of God expressed in us.
I like this illustration because it captures the diversity of function within the trinity. The Father activates, like the source of a song. The Son accomplishes, like a score written. The Spirit animates, like the sound produced.
Our world is filled with music because our world was made by God. Each time you hear music playing, each time you sing or play music yourself, each time you worship the Holy God through music, remember that that music has a source, a score, and a sound. And so does God in you.
With this in mind, listen again to this.