Laughter is the human form of purring

I've noticed that when I laugh my cat purrs. It makes her happy to see me happy.

Frequency analysis is in order.

It's a good comparison, but purring is ALSO a vibration that helps a cat to recover and rebuild tissue, it soothingly establishes a body frequency. At one point I needed to relearn how to sleep (after a time of great stress, work and personal) Sleeping with a cat, sometimes purring, outside of the city rewired my system and I learned how to sleep again.
Laughter and it's endorphins are also a healing mechanism for people, but it's aint like purring.

laughter is usually sick and sadistic relief of anger and rage, and horror and crying.

it's a moment you think it's all ok, it's all past.

but it never is. death is coming for you. Death will laugh in your face as you cry for eternity