Fixed-point (not floating point!) Mandelbrot generator in Hoon.

mandelbrot.hoon

::  Mandelbrot implementation inspired by the fixed-point version for
::  uBasic/4tH, and the floating point version for PureBasic from
::  https://rosettacode.org/wiki/Mandelbrot_set. This is pure fixed-point.
::
::  The trick is to use 10.000 as "floating" 1.0, and then do all math in terms
::  of that.
::
|%
++  left-edge    -21.000
++  right-edge   --15.000
++  top-edge     --15.000
++  bottom-edge  -15.000
::
++  max-iterations    254
::
+$  render-type  [r=@ g=@ b=@]
::
++  to-si
  |=  x=@u
  ^-  @si
  (pro:si (sun:si x) --10.000)
::
++  add-fp
  |=  [a=@s b=@s]
  (sum:si a b)
::
++  sub-fp
  |=  [a=@s b=@s]
  (dif:si a b)
::
++  mul-fp
  |=  [a=@s b=@s]
  (fra:si (pro:si (fra:si a --10) b) --1.000)
::
::  returns a fraction where when over=0, fp-fraction=0 and when over=under,
::  fp-fraction=--10.000
++  fraction-fp
  |=  [over=@s under=@s]
  (fra:si (pro:si over --10.000) under)
--
::
=/  plasma-colors=(list render-type)
  :: color map derived from matplotlib's
  :~  [12 7 134]  [16 7 135]  [19 6 137]  [21 6 138]  [24 6 139]
      [27 6 140]  [29 6 141]  [31 5 142]  [33 5 143]  [35 5 144]
      [37 5 145]  [39 5 146]  [41 5 147]  [43 5 148]  [45 4 148]
      [47 4 149]  [49 4 150]  [51 4 151]  [52 4 152]  [54 4 152]
      [56 4 153]  [58 4 154]  [59 3 154]  [61 3 155]  [63 3 156]
      [64 3 156]  [66 3 157]  [68 3 158]  [69 3 158]  [71 2 159]
      [73 2 159]  [74 2 160]  [76 2 161]  [78 2 161]  [79 2 162]
      [81 1 162]  [82 1 163]  [84 1 163]  [86 1 163]  [87 1 164]
      [89 1 164]  [90 0 165]  [92 0 165]  [94 0 165]  [95 0 166]
      [97 0 166]  [98 0 166]  [100 0 167]  [101 0 167]  [103 0 167]
      [104 0 167]  [106 0 167]  [108 0 168]  [109 0 168]  [111 0 168]
      [112 0 168]  [114 0 168]  [115 0 168]  [117 0 168]  [118 1 168]
      [120 1 168]  [121 1 168]  [123 2 168]  [124 2 167]  [126 3 167]
      [127 3 167]  [129 4 167]  [130 4 167]  [132 5 166]  [133 6 166]
      [134 7 166]  [136 7 165]  [137 8 165]  [139 9 164]  [140 10 164]
      [142 12 164]  [143 13 163]  [144 14 163]  [146 15 162]  [147 16 161]
      [149 17 161]  [150 18 160]  [151 19 160]  [153 20 159]  [154 21 158]
      [155 23 158]  [157 24 157]  [158 25 156]  [159 26 155]  [160 27 155]
      [162 28 154]  [163 29 153]  [164 30 152]  [165 31 151]  [167 33 151]
      [168 34 150]  [169 35 149]  [170 36 148]  [172 37 147]  [173 38 146]
      [174 39 145]  [175 40 144]  [176 42 143]  [177 43 143]  [178 44 142]
      [180 45 141]  [181 46 140]  [182 47 139]  [183 48 138]  [184 50 137]
      [185 51 136]  [186 52 135]  [187 53 134]  [188 54 133]  [189 55 132]
      [190 56 131]  [191 57 130]  [192 59 129]  [193 60 128]  [194 61 128]
      [195 62 127]  [196 63 126]  [197 64 125]  [198 65 124]  [199 66 123]
      [200 68 122]  [201 69 121]  [202 70 120]  [203 71 119]  [204 72 118]
      [205 73 117]  [206 74 117]  [207 75 116]  [208 77 115]  [209 78 114]
      [209 79 113]  [210 80 112]  [211 81 111]  [212 82 110]  [213 83 109]
      [214 85 109]  [215 86 108]  [215 87 107]  [216 88 106]  [217 89 105]
      [218 90 104]  [219 91 103]  [220 93 102]  [220 94 102]  [221 95 101]
      [222 96 100]  [223 97 99]  [223 98 98]  [224 100 97]  [225 101 96]
      [226 102 96]  [227 103 95]  [227 104 94]  [228 106 93]  [229 107 92]
      [229 108 91]  [230 109 90]  [231 110 90]  [232 112 89]  [232 113 88]
      [233 114 87]  [234 115 86]  [234 116 85]  [235 118 84]  [236 119 84]
      [236 120 83]  [237 121 82]  [237 123 81]  [238 124 80]  [239 125 79]
      [239 126 78]  [240 128 77]  [240 129 77]  [241 130 76]  [242 132 75]
      [242 133 74]  [243 134 73]  [243 135 72]  [244 137 71]  [244 138 71]
      [245 139 70]  [245 141 69]  [246 142 68]  [246 143 67]  [246 145 66]
      [247 146 65]  [247 147 65]  [248 149 64]  [248 150 63]  [248 152 62]
      [249 153 61]  [249 154 60]  [250 156 59]  [250 157 58]  [250 159 58]
      [250 160 57]  [251 162 56]  [251 163 55]  [251 164 54]  [252 166 53]
      [252 167 53]  [252 169 52]  [252 170 51]  [252 172 50]  [252 173 49]
      [253 175 49]  [253 176 48]  [253 178 47]  [253 179 46]  [253 181 45]
      [253 182 45]  [253 184 44]  [253 185 43]  [253 187 43]  [253 188 42]
      [253 190 41]  [253 192 41]  [253 193 40]  [253 195 40]  [253 196 39]
      [253 198 38]  [252 199 38]  [252 201 38]  [252 203 37]  [252 204 37]
      [252 206 37]  [251 208 36]  [251 209 36]  [251 211 36]  [250 213 36]
      [250 214 36]  [250 216 36]  [249 217 36]  [249 219 36]  [248 221 36]
      [248 223 36]  [247 224 36]  [247 226 37]  [246 228 37]  [246 229 37]
      [245 231 38]  [245 233 38]  [244 234 38]  [243 236 38]  [243 238 38]
      [242 240 38]  [242 241 38]  [241 243 38]  [240 245 37]  [240 246 35]
      [239 248 33]
  ==
::
|%
++  mandelbrot
  |=  [width=@u height=@u]
  ^-  (list (list render-type))
  ::  Internally, we emulate floating point numbers by having 1 equal
  ::  --10.000. This means we want to precompute the incoming values in that
  ::  coordinate space.
  ::
  =/  signed-width=@s  (to-si width)
  =/  signed-height=@s  (to-si height)
  ::
  =/  width-pixels  (gulf 0 (sub width 1))
  ::
  %+  turn  (gulf 0 (sub height 1))
  |=  y=@u
  ~&  [%cal-row y (sub height 1)]
  %+  turn  width-pixels
  |=  x=@u
  (calc-pixel (to-si x) (to-si y) signed-width signed-height)
::
++  calc-pixel
  |=  [scr-x=@s scr-y=@s width=@s height=@s]
  ^-  render-type
  ::
  =/  cr=@s  (sub-fp (mul-fp (fraction-fp scr-x width) --25.000) --20.000)
  =/  ci=@s  (sub-fp (mul-fp (fraction-fp scr-y height) --25.000) --12.500)
  ::
  =/  i=@    0
  =/  x0=@s  --0
  =/  y0=@s  --0
  ::
  |-
  ?:  (gte i max-iterations)
    (calculate-color-for 255)
  ::
  =/  xx=@s  (mul-fp x0 x0)
  =/  yy=@s  (mul-fp y0 y0)
  ::
  ?:  =(--1 (cmp:si (add-fp xx yy) --40.000))
    (calculate-color-for i)
  ::
  =/  xtemp=@s  (add-fp (sub-fp xx yy) cr)
  =.  y0        (add-fp (pro:si --2 (mul-fp x0 y0)) ci)
  =.  x0        xtemp
  ::
  $(i +(i))
::
++  calculate-color-for
  |=  o=@
  ^-  render-type
  ?:  =(o 255)
    [0 0 0]
  (snag o plasma-colors)
--
::
::  Generator usage:
::
::    @file/ppm +mandelbrot <width> <height>
::
:-  %say
|=  [^ [w=@ud h=@ud ~] ~]
:-  %atom
=/  mandelbrot-data  (mandelbrot w h)
::
%-  of-wain:format
^-  wain
%+  weld
  :~  'P3'
      (crip "{<w>} {<h>}")
      '255'
  ==
%+  turn  mandelbrot-data
|=  y=(list render-type)
^-  cord
%-  crip
%-  zing
%+  turn  y
|=  render-type
"{<r>} {<g>} {<b>} "

Attaching the raw PPM didn't work; Github didn't treat it as an image. Trying after converting it to a PNG:

You can fish the raw PPM out of this gist's history if you're interested.

Also, I made mostly stylistic changes to clean up the codebase for release AFTER I generated the above image.