### Exponential map transform

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#### Exponential map transform

« 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/btransform:    if @ison      c = #pixel      dc = a*(exp(-1i*b/w*(c-c0)))      #pixel = c0+dc    endifdefault:  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}

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