Iterated function: Difference between revisions

Revision as of 21:23, 21 March 2025

Revision as of 14:52, 18 May 2025

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[[File:Sine_iterations.svg|right|thumb|380px|

Iterates of the sine function (<span style="color:blue">blue</span>), in the first half-period. Half-iterate (<span style="color:orange">orange</span>), i.e., the sine's functional square root; the functional square root of that, the quarter-iterate (black) above it; and further fractional iterates up to the 1/64th. The functions below the (<span style="color:blue">blue</span>) sine are six integral iterates below it, starting with the second iterate (<span style="color:red">red</span>) and ending with the 64th iterate. The <span style="color:green">green</span> envelope triangle represents the limiting null iterate, thea sawtooth[[triangular function]] serving as the starting point leading to the sine function. The dashed line is the negative first iterate, i.e. the inverse of sine (arcsin).

(From the general pedagogy web-site.<ref>Curtright, T. L. [http://www.physics.miami.edu/~curtright/Schroeder.html Evolution surfaces and Schröder functional methods.]</ref> For the notation, see [http://www.physics.miami.edu/~curtright/TheRootsOfSin.pdf].)

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