Palindromic Expression for Phi: Difference between revisions
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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 < | 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 <syntaxhighlight lang=apl inline>⍣≡</syntaxhighlight>:<ref>Dyalog. [https://dfns.dyalog.com/n_limit.htm Function power limit (fixpoint)]. [[Dfns workspace]]. 2019-02-07.</ref> | ||
< | <syntaxhighlight lang=apl> | ||
limit←{ ⍝ Function power limit (fixpoint). | limit←{ ⍝ Function power limit (fixpoint). | ||
⍵ ⍺⍺{ ⍝ 'old' value: | ⍵ ⍺⍺{ ⍝ 'old' value: | ||
| Line 9: | Line 9: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
[[John Scholes]] noted that it was close to being a [[wikipedia:palindrome|palindrome]], so he inlined it and he amended it with dummy code to make its invocation for finding the [[wikipedia:golden ratio|golden ratio]] even closer to palindromic: | [[John Scholes]] noted that it was close to being a [[wikipedia:palindrome|palindrome]], so he inlined it and he amended it with dummy code to make its invocation for finding the [[wikipedia:golden ratio|golden ratio]] even closer to palindromic: | ||
< | <syntaxhighlight lang=apl> | ||
1{1+÷⍵}{⍵ ⍺⍺{⍺≡⍵:⍵ ⋄ ⍵ ⍺⍺ ∇∇ ⍺⍺ ⍵ ⋄ ⍵:⍵≡⍺}⍺⍺ ⍵}{⍵÷+1}1 | 1{1+÷⍵}{⍵ ⍺⍺{⍺≡⍵:⍵ ⋄ ⍵ ⍺⍺ ∇∇ ⍺⍺ ⍵ ⋄ ⍵:⍵≡⍺}⍺⍺ ⍵}{⍵÷+1}1 | ||
1.618033989 | 1.618033989 | ||
Latest revision as of 22:25, 10 September 2022
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.