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Are multiple hashtags allowed in NestList usage? If yes, how to implement it?

Example,

 f[{x_, y_}] := {x + y, x - y};
 NestList[f, {100, 75}, 5]

My attempt,

 NestList[{#1+#2,#1-#2} &,{100,75},5]

It does not work.

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4 Answers 4

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Use Apply.

NestList[Apply[{#1 + #2, #1 - #2} &], {100, 75}, 5]
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The argument being supplied to the function is a list. It's a single argument with head List. So, #2 cannot be bound to anything. You can either use Apply (per cvgmt's answer) or use Part:

NestList[{#[[1]] + #[[2]], #[[1]] - #[[2]]} &, {100, 75}, 5]
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NestList[{{1, 1}, {1, -1}}.# &, {100, 75}, 5]
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Use Function and Apply:

NestList[Apply[Function[{x, y}, {x + y, x - y}]], {100, 75}, 5]
(*{{100, 75}, {175, 25}, {200, 150}, {350, 50}, {400, 300}, {700, 100}}*)

Or following your attempt:

f := Function[{x, y}, {x + y, x - y}]
NestList[Apply[f], {100, 75}, 5]
(*{{100, 75}, {175, 25}, {200, 150}, {350, 50}, {400, 300}, {700, 100}}*)

Or you can define your function as a solution rule and use the resource function SolutionRulesToFunctions as follows:

ReplaceAll[ResourceFunction["SolutionRulesToFunctions"][f[{x, y}] -> {x + y, x - y}]][NestList[Apply[f], {100, 75}, 5]]
(*{{100, 75}, {175, 25}, {200, 150}, {350, 50}, {400, 300}, {700, 100}}*)
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