Question

Why do Lord Vishnu and Lord Shiva always meditate on each other?

Answer

I would try to correct a one misconception that Lord Vishnu meditates on Lord Shiva. No he doesn't, Lord Vishnu actually meditates on Lord Brahma.

It is a cyclic process, Lord Brahma meditates on Lord Shiva, Lord Shiva meditates on Lord Vishnu and Lord Vishnu meditates on Lord Brahma, and the cycle goes on.

Why this Cycle ? Brahma is a creator by nature, but before creation there is destruction, so he needs to understand the destruction, therefore he meditates on Lord Shiva, Vishnu is a Preserver, to Preserve he needs to understand the generation(creation), therefore he meditates on Lord Brahma , Shiva on the other-hand is a annihilator, to destroy he needs to understand Preservation, therefore he meditates on Lord Vishnu.

Why they need to understand their predecessor process ? Natural law, every process is the outcome of a process, and to understand a process, you need to know origin process. This also shows the cyclic and infinitum nature of any process's existence. This is a reason why science went way back to atoms, then to neutrons and still searching the cause of it(currently medalling with string theory).

To make everything more visible, I created this image which conveys it all. In the image, B = Brahma, V = Vishnu and S = Shiva.

enter image description here

But is it not written in Puranas ? Yes its written, but in other way, puranas say :

Lord Vishnu worships Lord Shiva and Lord Shiva worships Lord Raam (Vishnu Avatar).

But meditation is different than worshiping. Lord Shiva cursed Lord Brahma that he would not be worshiped by anyone. Meditation is needed to understand something, you want to understand 'BIKE' meditate on it, you want to understand 'GOD' meditate on him. Worshiping is kind of give-take relationship between Purusha and Prakrati, the prakrati worships Purusha, to get something from it. Some worship Purusha to easily understand the way(the creation or the God), because meditating can sometime become tougher and time lengthy and needs higher consciousness.

About the Serial ?

TV serial "Devo ke Dev Mahadev" on channel "Life Ok", also told the same thing, that Vishnu actually meditates on Bhrama, It is in 8th October 2012, 234th episode.

The scene describes that Mata Parvati comes across Lord Shiva, who is meditating on Lord Vishnu at that time, she asks him the question why he meditating on Lord Vishnu, and their he answers about the cycle process.

Note: “The question: Why do Lord Vishnu and Lord Shiva always meditate on each other?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.