4 ms·

His first examples g1, g2 are not shifts of f. What am I missing.

• cjhanks 9y ago
  The limit of `g_i / f` is also not 1. I think he's just looking for convergent functions.
  • c517402 9y ago
    Perhaps you meant “convergent function ratios.” The first example equations are parabolas (divergent).
    • cjhanks 9y ago
      Yes.
• c517402 9y ago
  From the first sentence of the paper: “I explore functions f that can be written as a sum f=g1+g2 where g1 and g2 are shifted and possibly reflected versions of each other, both strongly resembling the original function f.” Note, not f but “both strongly resembling the original function f.”
• tylerneylon 9y ago
  You're right that the g1 and g2 in section 2 are also scaled in addition to being shifts of f. I plan to clarify this in the text. This work is inspired by the self-similarity of fractals, which is in some cases primarily an intuitive or informal idea: for example, the Mandelbrot set is considered self-similar, but I'm not aware (despite searching) of any simple automorphisms of the Mandelbrot.
  • gergoerdi 9y ago
    There's this local example in Wikipedia: https://en.wikipedia.org/wiki/Mandelbrot_set#/media/File:Mandelbrot_zoom.gif https://en.wikipedia.org/wiki/Mandelbrot_set#/media/File:Man...