Powers of Phi and Fibonacci Sequence

Yesterday, I noticed a pattern in the Powers of Phi and the Fibonacci Sequence:

Phi¹ = Phi
Phi² = Phi(0+1Phi)
Phi³ = Phi(1+1Phi)
Phi⁴ = Phi(1+2Phi)
Phi⁵ = Phi(2+3Phi)
Phi⁶ = Phi(3+5Phi)
Phi⁷ = Phi(5+8Phi)
Phi⁸ = Phi(8+13Phi)
Phi⁹ = Phi(13+21Phi)
Phi¹⁰ = Phi(21+34Phi)
Phi¹¹ = Phi(34+55Phi)
Phi¹² = Phi(55+89Phi)

I thought this was an interesting and novel expression of the powers of Phi and the Fibonacci sequence. From what I can tell, so far, nobody else has noticed this pattern previously.

7/3/6 - Today I extended the above relationship into a type of multiplication table for powers of Phi. Check the link above to see the full table.