# Palindromic Expression for Phi

Some find that APL expressions can have a poetic beauty. Phil Last submitted the following variable-free recursive dfn to compute the limit of a converging function, equivalent to the derived monadic operator `⍣≡`:[1]

```limit←{             ⍝ Function power limit (fixpoint).
⍵ ⍺⍺{           ⍝ 'old' value:
⍺≡⍵:⍵       ⍝       old matches new: finished.
⍵ ∇ ⍺⍺ ⍵    ⍝       otherwise: try new value.
}⍺⍺ ⍵           ⍝ 'new' value.
}```

John Scholes noted that it was close to being a palindrome, so he inlined it and he amended it with dummy code to make its invocation for finding the golden ratio even closer to palindromic:

```      1{1+÷⍵}{⍵ ⍺⍺{⍺≡⍵:⍵ ⋄ ⍵ ⍺⍺ ∇∇ ⍺⍺ ⍵ ⋄ ⍵:⍵≡⍺}⍺⍺ ⍵}{⍵÷+1}1
1.618033989```

Scholes then published a minute-long video with musical accompaniment where he types the expression in a symmetric fashion, culminating with the execution.[2]

## References

1. Dyalog. Function power limit (fixpoint). Dfns workspace. 2019-02-07.
2. DFunctionista. Palindromic Expression for Phi in APL. YouTube. 2009-02-13.