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  "body": "\n## Summary\n\nAn infinite composition is the limit of the finite compositions $f_1 \\circ f_2 \\circ \\cdots \\circ f_n$, or of $f_n \\circ \\cdots \\circ f_1$, of a sequence of functions.\nIt extends [[function composition|0THBK9V825]] to infinitely many factors, in the same way as a series extends a finite sum.\nContinued fractions, nested radicals and power towers are all infinite compositions.\nIteration of a single function is the special case where all $f_n$ are equal.\n\n## Explanations\n\n### L1 human\n\nFeed a starting value into $f_n$, feed the result into $f_{n-1}$, and so on down to $f_1$.\nDoing this for larger and larger $n$ gives a sequence of numbers, and the infinite composition is its limit when it exists.\nFor example, the continued fraction $\\cfrac{1}{2 + \\cfrac{1}{2 + \\cdots}}$ comes from composing the maps $w \\mapsto \\frac{1}{2 + w}$ and evaluating at $0$.\n",
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