Alex Schroeder/Island Generation

For a map generator of mine I needed to prototype an island generation algorithm. Inspired by archipelagos like Hawaii and the Galapagos, I wanted the following:

• a hot spot moves across the map, lifting land up
• behind the hot spot, land starts sinking again
• the uplift is spotty because there are volcanoes, and parasitic cones, etc. It's not always clear where the land gets lifted
• the sinking is also spotty because hard lava cores can be left behind, softer material gets eroded, crusts break and sink
• the sinking must be somewhat slower than the rising or else there won't be much of an island chain to see

J901 version

mx =: 30
my =: 20

NB. a table of complex numbers
c =: (i. my) j./ i. mx

NB. starting position of the hotspot
hr =: 6
hy =: >. hr % 2
hx =: <. 0.5 + (my % 3) + ? <. 0.5 + my % 3
hc =: hx j. hy

NB. a function to compute altitude changes based on where the hotspot is
change =: 3 : 0
  h =. hr > {. & *. c - y     NB. hotspot = 1
  u =. 0.85 < ? (my, mx) $ 0  NB. regions atop the hotspot might move up
  d =. 0.7 < ? (my, mx) $ 0  NB. regions off the hotspot might move down
  (u * h) - d * -. h
)

NB. a biased list of steps to take
d =: _1j1 1j1 0j1

NB. a table of altitudes
a =: (my, mx) $ 0

NB. compute the meandering path of the hotspot across the map
NB. compute the change for each step and add it to the altitude
NB. no negative values
3 : 0''
for. i. mx - 2  * hr do.
  hc =: hc+(?#d){d
  a =: 0 & >. a + change hc
end.
)

decimal =:16"_#.'0123456789abcdef'"_ i.]

rgb =: 3 : 0
  n =. decimal }. y     NB. strip leading #
  (<.n % 65536), ((<.n % 256) |~ 256), (n |~ 256)
)
ocean  =: rgb '#1c86ee' NB. 0
water  =: rgb '#6ebae7' NB. 1
sand   =: rgb '#e3bea3' NB. 2
dry    =: rgb '#c97457' NB. 3
nice   =: rgb '#b0b446' NB. 4
green  =: rgb '#77904c' NB. 5
humid  =: rgb '#2d501a' NB. 6
rocky  =: rgb '#dcddbe' NB. 7
colors =: (ocean, water, sand, dry, nice, green, humid,: rocky)
colors viewmat a

iPad version

mx =: 30
my =: 20

NB. a table of complex numbers
c =: (i. my) j./ i. mx

NB. a table of altitudes
a =: (my, mx) $ _2

NB. center of the hotspot
hr =: 5
hy =: >. hr % 2
hx  =: <. 0.5 + (my % 3) + ? <. 0.5 + my % 3
hc =: hx j. hy

NB. a list of translations
d =: _1j0 1j0, 4 $ 0j1
m =: ( ? 30 # # d ) { d

NB. start loop
3 : 0''
for_i. m do.
  hc =: hc + i               NB. move hotspot center
  h =: 5 > {. & *. c - hc    NB. hotspot = 1
  l =: -. _2 = a * -. h      NB. outside the hotspot -2 is the limit
  r =: 0.8 < ? (my, mx) $ 0  NB. 20% of regions are potentially active
  s =: 0.5 < ? (my, mx) $ 0  NB. 50% of regions...
  t =: h + s * -. h          NB. ...will ignore the activity
  a =: a + r * t* l * _1 + 2 * h
end.
)

jv a