# Palindromic Expression for Phi

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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

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