Exponential map transform

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Offline gerrit

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« on: August 05, 2018, 05:02:17 AM »
Not much activity here, UF seems to be unpopular here. Here's a UF transformation formula implementing the "exponential map": https://fractalforums.org/fractal-movie-gallery/19/emndl-vs-nanomb-mandelbrot-set-zooms/1691/msg8575#new.

Output sample is random zoom past a few minibrots and making a tree.

Code: [Select]
ExponentialMap {
;
; Vertical exponential transform.
; Make narrow high window (say 100X800), zoom, put point of interest at bottom.
; Turn on. Tweak with the 2 controls, and select appropriate width (depends on image,
; narrower for deeper zooms).
;
global:
  if (4 * #height < 3 * #width)
    pixeldim = 3/#magn/#height
  else
    pixeldim = 4/#magn/#width
  endif
  w = #width * pixeldim
  h = #height * pixeldim
  cc = #center
  c0 = cc - 1i/2 * h +0i*w -w/4 * @sh
  b = w/h*log(#magn) *@b
  a = 1i*w/b
transform:
    if @ison
      c = #pixel
      dc = a*(exp(-1i*b/w*(c-c0)))
      #pixel = c0+dc
    endif
default:
  title = "Exponential map"
  param ison
    caption = "On"
    default = false
  endparam
  float param b
    caption = "vert. control"
    default = 1.2
  endparam
  float param sh
    caption = "hor. shift"
    default = 0
  endparam
}


Linkback: https://fractalforums.org/ultrafractal/59/exponential-map-transform/1697/


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