Talk:Infinite compositions of analytic functions
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OK, I've put in some links, so this should no longer be an orphan. I'll be working on this for a while. As a separate general topic it is a relatively new line of research (1960s -), except for earlier work in the analytic theory of continued fractions. I will demonstrate the connections to continued fractions, series, and other more exotic infinite expansions in time. Comments are welcome. Oldtimermath (talk) 02:47, 20 February 2012 (UTC)
I appreciate efforts to improve this page. However, when such efforts produce a product that is inferior to what I have posted (using MathType) in favor of some sort of ideal coding I question whether such efforts are truly benign. Oldtimermath (talk) 04:17, 6 July 2016 (UTC)
I just wanted to say that some of the pictures here are absolutely gorgeous. :) JonathanHopeThisIsUnique (talk) 04:08, 3 December 2017 (UTC)
A version of one of the reference papers with added imagery:
A Primer on the Elementary Theory of Infinite Compositions of Complex Functions with Imagery
A collection of published and unpublished papers/notes on this subject can be found here:[1]. Oldtimermath (talk) 03:54, 12 April 2022 (UTC)
Explanation of pictures
[edit]Although the pictures are interesting to look at, the article needs to include an explanation of what the pictures are showing.
What do the different colors indicate? 2601:200:C000:1A0:C89F:AFD1:7BA3:8396 (talk) 19:33, 9 October 2022 (UTC)
- In a designated rectangle in the complex plane the BASIC program goes down columns and across rows, point by point, iterating each complex number (point) by a sequence of functions as described in the article a specific number of times, say, fifty iterations. Then the resulting value of the modulus determines what color the point is painted. Black and grey at or near zero, then dark to light shades of red, then shades of green, finally shades of blue for very large moduli. Arguments play no role. For monochrome images the same process but in shades of grey. Then color added via Photoshop. Oldtimermath (talk) 04:36, 28 October 2022 (UTC)