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Palindromic Expression for Phi: Difference between revisions
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Palindromic Expression for Phi (view source)
Revision as of 22:25, 10 September 2022
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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: | ||
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</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 | ||