File:Uf109.jpg

English: the exponential map: random zoom past a few minibrots and making a tree. Below is Ultrafractal transformation formula implementing the "exponential map ( file with .uxf extension)

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
}