No, I don't think the Doctrine of the Trinity has ever been explained as a natural phenomenon after reading the Bible. There are places where all three Persons of the Trinity are mentioned together, like the great commission
Go therefore, Baptizing in the name of the Father and of the Son and of the Holy Spirit
and there's other places where Our Lord mentions only Him and the Father being one.
I am in the father and the Father is in Me
no one knows the Father like the Son
I don't know if it is right to interpret that that means Jesus knows the Father in a way not even the Holy Spirit can know Him.
Finally, there is a question of who sent who.
... the Father who sent me.
Behold, I am sending the Paraclete (Holy Spirit)
who sent who is very important to the doctrine of the trinity, but it never got anyone in hot water until 600 years after the doctrine was formalized and accepted by most Christians as it continues to be today.
So, the Church finished the Bible in the 4th Century and 200 years later finalized the Doctrine of the Trinity at the council of Chalcedon numerous other ways of coming up with interpretations of Gods nature were quashed there and one Universal interpretation was applied to everyone who wanted to be in good standing with the church.
Some people didn't get the memo and some people killed the memo bringers and some memos were so badly scorched in the desert that by the time they got it 200 years later, they called it Islam. But, no the Trinity is not reasonable and its not inherently Biblical. It takes Faith in the Church to believe in the Trinity.