Lua - Perlin Noise Generation - Getting bars rather than squares

Question

I'm currently learning Löve 2d/Lua and trying my hand at generating noise using the Perlin Noise algorithm.

I've adapted Ken Perlin's Improved Noise code here:

Code edited with fixes per Doug's answer

-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/

perlin = {}
perlin.p = {}
perlin.permutation = { 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
}
perlin.size = 256
perlin.gx = {}
perlin.gy = {}
perlin.randMax = 256

function perlin:load(  )
    for i=1,self.size do
        self.p[i] = self.permutation[i]
        self.p[256+i] = self.p[i]
    end
end

function perlin:noise( x, y, z )
    local X = math.floor(x) % 256
    local Y = math.floor(y) % 256
    local Z = math.floor(z) % 256
    x = x - math.floor(x)
    y = y - math.floor(y)
    z = z - math.floor(z)
    local u = fade(x)
    local v = fade(y)
    local w = fade(z)
    local A  = self.p[X+1]+Y
    local AA = self.p[A+1]+Z
    local AB = self.p[A+2]+Z
    local B  = self.p[X+2]+Y
    local BA = self.p[B+1]+Z
    local BB = self.p[B+2]+Z

    return lerp(w, lerp(v, lerp(u, grad(self.p[AA+1], x  , y  , z  ),
                                   grad(self.p[BA+1], x-1, y  , z  )),
                           lerp(u, grad(self.p[AB+1], x  , y-1, z  ),
                                   grad(self.p[BB+1], x-1, y-1, z  ))),
                   lerp(v, lerp(u, grad(self.p[AB+2], x  , y  , z-1),
                                   grad(self.p[BA+2], x-1, y  , z-1)),
                           lerp(u, grad(self.p[AB+2], x  , y-1, z-1),
                                   grad(self.p[BB+2], x-1, y-1, z-1))))
end

function fade( t )
    return t * t * t * (t * (t * 6 - 15) + 10)
end

function lerp( t, a, b )
    return a + t * (b - a)
end

function grad( hash, x, y, z )
    local h = hash % 16
    local u = h < 8 and x or y
    local v = h < 4 and y or ((h == 12 or h == 14) and x or z)
    return ((h % 2) == 0 and u or -u) + ((h % 3) == 0 and v or -v)
end

and here's my main.lua Löve script:

require 'noise'

function love.load(  )
    perlin:load()
    -- love.graphics.setBackgroundColor(255, 255, 255)
    love.window.setMode(500, 500)
end

function love.update( dt )

end

function love.draw(  )
    for i=1,500 do
        for j=1,500 do
            local x = perlin:noise(i/10, j/10, 0.3)
            love.graphics.setColor(math.floor(x*255), math.floor(x*255), math.floor(x*255))
            love.graphics.rectangle("fill", 5*(i-1), 5*(j-1), 5, 5)
        end
    end
end

The problem I'm encountering is that rather than getting a nice image of pseudorandom squares, I'm getting some gradient-like bars like this:

I'm pretty stumped as to why I'm not getting the usual noise rendering.

EDIT: Here's the working rendering!

Fruma

Answer 1

One problem:

local X = math.floor(x) and 255
local Y = math.floor(y) and 255
local Z = math.floor(z) and 255

should be

local X = math.floor(x) & 255
local Y = math.floor(y) & 255
local Z = math.floor(z) & 255

assuming you have Lua 5.3.x. If you have an earlier version of Lua, there are bitwise libraries that may or may not be available for Löve. So, in this case you can use:

local X = math.floor(x) % 256
local Y = math.floor(y) % 256
local Z = math.floor(z) % 256

Explanation: The conjunction operator and returns its first argument if this value is false or nil; otherwise, and returns its second argument.

Orchitis

Thank you, thank you! I searched the Lua docs prior to posting and couldn't find anything about bitwise operations, so this was very helpful in clearing things up! Especially since Love uses Lua 5.1, so I don't have access to 5.2 or 5.3 even if I wanted. – Fruma

Answer 2

You're using and to replace & (bitwise and), I've updated your example below (using the BitAND method from Lua - Bitwise Logical Operations), and replaced the places where you've used and which includes the initial declaration or X, Y, Z in perlin:load and the declaration of h in grad. I've tested it using love and the output looks correct.

-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/
local function BitAND(a,b)--Bitwise and
    local p,c=1,0
    while a>0 and b>0 do
        local ra,rb=a%2,b%2
        if ra+rb>1 then c=c+p end
        a,b,p=(a-ra)/2,(b-rb)/2,p*2
    end
    return c
end

perlin = {}
perlin.p = {}
perlin.permutation = { 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
}
perlin.size = 256
perlin.gx = {}
perlin.gy = {}
perlin.randMax = 256

function perlin:load(  )
    for i=1,self.size do
        self.p[i] = self.permutation[i]
        self.p[255+i] = self.p[i]
    end
end

function perlin:noise( x, y, z )
    local X = BitAND(math.floor(x), 255) + 1
    local Y = BitAND(math.floor(y), 255) + 1
    local Z = BitAND(math.floor(z), 255) + 1

    x = x - math.floor(x)
    y = y - math.floor(y)
    z = z - math.floor(z)
    local u = fade(x)
    local v = fade(y)
    local w = fade(z)
    local A  = self.p[X]+Y
    local AA = self.p[A]+Z
    local AB = self.p[A+1]+Z
    local B  = self.p[X+1]+Y
    local BA = self.p[B]+Z
    local BB = self.p[B+1]+Z

    return lerp(w, lerp(v, lerp(u, grad(self.p[AA  ], x  , y  , z  ),
                                   grad(self.p[BA  ], x-1, y  , z  )),
                           lerp(u, grad(self.p[AB  ], x  , y-1, z  ),
                                   grad(self.p[BB  ], x-1, y-1, z  ))),
                   lerp(v, lerp(u, grad(self.p[AA+1], x  , y  , z-1),
                                   grad(self.p[BA+1], x-1, y  , z-1)),
                           lerp(u, grad(self.p[AB+1], x  , y-1, z-1),
                                   grad(self.p[BB+1], x-1, y-1, z-1))))
end


function fade( t )
    return t * t * t * (t * (t * 6 - 15) + 10)
end

function lerp( t, a, b )
    return a + t * (b - a)
end

function grad( hash, x, y, z )
    local h = BitAND(hash, 15)
    local u = h < 8 and x or y
    local v = h < 4 and y or ((h == 12 or h == 14) and x or z)
    return ((h and 1) == 0 and u or -u) + ((h and 2) == 0 and v or -v)
end

Ulphiah