2013-01-08 17:05:54 +00:00
|
|
|
module Flame where
|
|
|
|
|
|
|
|
import Random
|
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- Basic functions
|
|
|
|
|
|
|
|
-- nth element of a list
|
|
|
|
l !! n = if n == 0 then head l else (tail l) !! (n-1)
|
|
|
|
-- negative of a number (I don't like writing 0-x).
|
|
|
|
neg x = 0-x
|
|
|
|
|
|
|
|
-- Colors (theme is solarized)
|
2013-01-08 17:05:54 +00:00
|
|
|
base03 = rgb 0 43 54
|
|
|
|
base02 = rgb 7 54 66
|
|
|
|
base01 = rgb 88 110 117
|
|
|
|
base00 = rgb 101 123 131
|
|
|
|
base0 = rgb 131 148 150
|
|
|
|
base1 = rgb 147 161 161
|
|
|
|
base2 = rgb 238 232 213
|
|
|
|
base3 = rgb 253 246 227
|
|
|
|
yellow = rgb 181 137 0
|
|
|
|
orange = rgb 203 75 22
|
|
|
|
red = rgb 220 50 47
|
|
|
|
magenta = rgb 211 54 130
|
|
|
|
violet = rgb 108 113 196
|
|
|
|
blue = rgb 38 139 210
|
|
|
|
cyan = rgb 42 161 152
|
|
|
|
green = rgb 133 153 0
|
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- Default text color
|
2013-01-09 14:37:54 +00:00
|
|
|
mybase = rgba 108 113 196 (2/3)
|
2013-01-08 17:05:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- draw a point at position (x,y)
|
2013-01-09 14:37:54 +00:00
|
|
|
point = filled mybase . rect 1 1
|
2013-01-08 17:05:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- fill the background with color base3
|
2013-01-08 17:05:54 +00:00
|
|
|
background w h = filled base3 ( rect w h (div w 2,div h 2))
|
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- RANDOM PART
|
2013-01-08 17:05:54 +00:00
|
|
|
nextint n =
|
|
|
|
let
|
|
|
|
a = 22695477
|
|
|
|
c = 1
|
|
|
|
m = 2^32
|
|
|
|
in
|
|
|
|
(a*n + c) `rem` m
|
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- generate a random sequence of length k starting with some seed
|
2013-01-08 17:05:54 +00:00
|
|
|
randlist seed k = if (k<0) then [] else (nextint seed):randlist (nextint seed) (k-1)
|
2013-01-09 17:23:16 +00:00
|
|
|
|
|
|
|
-- generate a random sequence of points of length k starting with some seed
|
2013-01-08 17:05:54 +00:00
|
|
|
randcouples seed k = if (k<0) then []
|
|
|
|
else
|
|
|
|
let ns = nextint seed
|
|
|
|
nns = nextint ns
|
|
|
|
in (ns,nns):randcouples nns (k-1)
|
2013-01-09 17:23:16 +00:00
|
|
|
-- END OF PSEUDO RANDOM NUMBER GENERATION
|
|
|
|
|
|
|
|
|
|
|
|
{-
|
|
|
|
- Flame Set
|
|
|
|
-
|
|
|
|
- S = U_{i} F_i(S)
|
|
|
|
-
|
|
|
|
- F_i being transformations
|
|
|
|
- General form:
|
|
|
|
- F = affine . linearcomp [variation] . affine
|
|
|
|
- affine is a linear function (x,y) -> (ax+by+c,dx+ey+f)
|
|
|
|
- variation is some kind of function with some contraction properties
|
|
|
|
ex: (x,y) -> (x,y), (sin x, sin y), etc...
|
|
|
|
- linearcomp [f] is a linear composition of functions: (x,y) -> Sum vi*f(x,y)
|
|
|
|
-}
|
|
|
|
|
|
|
|
data Matrice = M Float Float Float Float Float Float
|
|
|
|
aff (M a b c d e f) (x,y) = (a*x + b*y + c, d*x + e*y +f)
|
|
|
|
|
|
|
|
-- Some affine functions to generate the sierpinsky set
|
|
|
|
-- Equivalent to
|
|
|
|
-- sierp = [ \(x,y)->(x/2,y/2)
|
|
|
|
-- , \(x,y)->((x+1)/2,y/2)
|
|
|
|
-- , \(x,y)->(x/2,(y+1)/2) ]
|
|
|
|
sierp = [ aff $ M
|
|
|
|
0.5 0.0 0.0
|
|
|
|
0.0 0.5 0.0
|
|
|
|
, aff $ M
|
|
|
|
0.5 0.0 0.5
|
|
|
|
0.0 0.5 0.0
|
|
|
|
, aff $ M
|
|
|
|
0.5 0.0 0.0
|
|
|
|
0.0 0.5 0.5
|
|
|
|
]
|
2013-01-08 17:05:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- Some variations
|
2013-01-09 14:37:54 +00:00
|
|
|
vs = [ \(x,y) -> (x,y)
|
|
|
|
, \(x,y) -> (sin x, sin y)
|
|
|
|
, \(x,y) -> let r2 = x*x+y*y in (x/r2,y/r2)
|
|
|
|
, \(x,y) -> let r2 = x*x+y*y in (x*(sin r2) - y*(cos r2),x*(cos r2) + y * (sin r2))
|
|
|
|
, \(x,y) -> let r = sqrt (x^2+y^2) in ((x - y)*(x + y)/r,2*x*y/r)
|
|
|
|
]
|
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- Some final functions
|
|
|
|
fs = [ (vs !! 3) . (sierp !! 0)
|
|
|
|
, (vs !! 3) . (sierp !! 1)
|
|
|
|
, (vs !! 3) . (sierp !! 2)]
|
2013-01-09 14:37:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- Transformation functions
|
|
|
|
-- translate
|
|
|
|
trans (tx,ty) = aff $ M 1 0 tx 0 1 ty
|
|
|
|
-- rotate
|
|
|
|
rot phi = aff $ M (cos phi) (sin phi) 0.0 (neg (sin phi)) (cos phi) 0.0
|
|
|
|
-- zoom
|
|
|
|
zoom z = aff $ M z 0 0 0 z 0
|
2013-01-09 14:37:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
-- The final transformation to transform the final result (zoom,rotate,translate)
|
|
|
|
final = trans (480,300) . zoom 500 . rot (neg 0.747)
|
2013-01-09 14:37:54 +00:00
|
|
|
|
|
|
|
sierpset startpoint rands =
|
|
|
|
if rands == []
|
|
|
|
then []
|
|
|
|
else
|
|
|
|
let
|
2013-01-09 17:23:16 +00:00
|
|
|
randval=(head rands) `rem` (length fs)
|
|
|
|
newpoint = (fs !! randval) startpoint
|
|
|
|
savepoint = final newpoint
|
2013-01-09 14:37:54 +00:00
|
|
|
in
|
2013-01-09 17:23:16 +00:00
|
|
|
savepoint:(sierpset newpoint (tail rands))
|
2013-01-09 14:37:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
concatmap f l = concat (map f l)
|
|
|
|
sierpinsky = drop 30 $ concatmap (\s -> sierpset (0.0,0.0) (randlist s 4000)) [1..5]
|
|
|
|
|
|
|
|
scene (x,y) (w,h) =
|
|
|
|
let
|
|
|
|
inpoint (x,y) = x>=0 && x<=w && y>=0 && y<=h
|
|
|
|
in collage w h $
|
|
|
|
background w h:
|
|
|
|
map point (filter inpoint sierpinsky)
|
2013-01-08 17:05:54 +00:00
|
|
|
|
2013-01-09 17:23:16 +00:00
|
|
|
main = scene <~ Mouse.position ~ Window.dimensions
|