--from https://github.com/thenumbernine/lua-simplexnoise/blob/master/2d.lua
--Mostly as a test, does not give same results as perlin but is designed to give patterns all the same

local Simplex = {}

-- 2D simplex noise

local grad3 = {
    {1,1,0},{-1,1,0},{1,-1,0},{-1,-1,0},
    {1,0,1},{-1,0,1},{1,0,-1},{-1,0,-1},
    {0,1,1},{0,-1,1},{0,1,-1},{0,-1,-1}
}

local  p = {151,160,137,91,90,15,
    131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
    190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
    88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
    77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
    102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
    135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
    5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
    223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
    129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
    251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
    49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
    138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180}
local perm = {}
for i=0,511 do
    perm[i+1] = p[bit32.band(i, 255) + 1]
end

local function dot(g, ...)
    local v = {...}
    local sum = 0
    for i=1,#v do
        sum = sum + v[i] * g[i]
    end
    return sum
end

local F2 = 0.5*(math.sqrt(3.0)-1.0)
local G2 = (3.0-math.sqrt(3.0))/6.0
function Simplex.d2(xin, yin,seed)
    xin = xin + seed
    yin = yin + seed
    local n0, n1, n2    -- Noise contributions from the three corners
    -- Skew the input space to determine which simplex cell we're in
    local s = (xin+yin)*F2; -- Hairy factor for 2D
    local i = math.floor(xin+s)
    local j = math.floor(yin+s)
    local t = (i+j)*G2
    local X0 = i-t -- Unskew the cell origin back to (x,y) space
    local Y0 = j-t
    local x0 = xin-X0 -- The x,y distances from the cell origin
    local y0 = yin-Y0
    -- For the 2D case, the simplex shape is an equilateral triangle.
    -- Determine which simplex we are in.
    local i1, j1 -- Offsets for second (middle) corner of simplex in (i,j) coords
    if x0 > y0 then
        i1 = 1
        j1 = 0 -- lower triangle, XY order: (0,0)->(1,0)->(1,1)
    else
        i1 = 0
        j1 = 1
    end-- upper triangle, YX order: (0,0)->(0,1)->(1,1)
    -- A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
    -- a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
    -- c = (3-sqrt(3))/6
    local x1 = x0 - i1 + G2 -- Offsets for middle corner in (x,y) unskewed coords
    local y1 = y0 - j1 + G2
    local x2 = x0 - 1 + 2 * G2 -- Offsets for last corner in (x,y) unskewed coords
    local y2 = y0 - 1 + 2 * G2
    -- Work out the hashed gradient indices of the three simplex corners
    local ii = bit32.band(i, 255)
    local jj = bit32.band(j, 255)
    local gi0 = perm[ii + perm[jj+1]+1] % 12
    local gi1 = perm[ii + i1 + perm[jj + j1+1]+1] % 12
    local gi2 = perm[ii + 1 + perm[jj + 1+1]+1] % 12
    -- Calculate the contribution from the three corners
    local t0 = 0.5 - x0 * x0 - y0 * y0
    if t0 < 0 then
        n0 = 0.0
    else
        t0 = t0 * t0
        n0 = t0 * t0 * dot(grad3[gi0+1], x0, y0) -- (x,y) of grad3 used for 2D gradient
    end
    local t1 = 0.5 - x1 * x1 - y1 * y1
    if t1 < 0 then
        n1 = 0.0
    else
        t1 = t1 * t1
        n1 = t1 * t1 * dot(grad3[gi1+1], x1, y1)
    end
    local t2 = 0.5 - x2 * x2 - y2 * y2
    if t2 < 0 then
        n2 = 0.0
    else
        t2 = t2 * t2
        n2 = t2 * t2 * dot(grad3[gi2+1], x2, y2)
    end
    -- Add contributions from each corner to get the final noise value.
    -- The result is scaled to return values in the interval [-1,1].
    return 70.0 * (n0 + n1 + n2)
end

return Simplex