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--
-- @description Creates a Mandelbrot set texture node.
-- @author      Stratified
-- @version     0.1
-- 
-- The code to generate the Mandelbrot set is a modified version of this code:
-- http://www.timestretch.com/article/mandelbrot_fractal_benchmark#aba942b3e0f9e50dd67b83d89ec88139
--

local BAILOUT        = 4 
local MAX_ITERATIONS = 1000

-- Checks if a pixel in the image plane is in the mandelbrot set.
-- Returns 0 if the pixel is not. The modulus of the last generated
-- complex number is returned when the thing is in the set
--
-- Boring theory:
-- A point c (complex number really) is in the Mandelbrot set if the series
-- generated by z(n+1) = z(n)^2 + c (with z(0) = 0 + j*0) is not going to infinity.
local function inMandelbrotSet(x, y)

	local cr = x
	local ci = y
	local zi = 0.0
	local zr = 0.0
	local k  = 0
	
	while 1 do
		k = k+1
        -- calculate z(n+1) from z(n)
		local zrzi2 = zr * zi * 2
		local zr2   = zr * zr
		local zi2   = zi * zi
		zr = zr2 - zi2 + cr
		zi = ci + zrzi2
        -- check if we're still bound, bail out if not
		if (zi2 + zr2 > 4) then
			return false
		end
		
        -- if we reached the maximum number of iterations and the last value
        -- of the generated series is still bounded, we assume the pixel is
        -- in the Mandelbrot set.
		if (k > MAX_ITERATIONS) then
            return true
		end
	end
end

-- Generates a Mandelbrot set centered around the centre of the image.
function genMandelbrotTex(w, h)

    -- create a data structure for the image
    local image  = {}
    image.size   = { w, h }
    image.type   = octane.image.type.LDR_RGBA
    image.buffer = {}

    -- see which pixels are in the Mandelbrot set
	for y = 0, h-1 do
		for x = 0, w-1 do
            -- transform x so it's in the range [-2, 1]
            local sx = 3 * (x / w) - 2
            -- transform y so it's in the range [-1, 1]
            local sy = 2 * (y / h) - 1

            local colour = inMandelbrotSet(sx, sy)
            -- colour pixels in the set
			if colour then
                table.insert(image.buffer, 255)
                table.insert(image.buffer, 127)
                table.insert(image.buffer, 0)
                table.insert(image.buffer, 0)
            -- pixels not in the set are black
			else
                table.insert(image.buffer, 0)
                table.insert(image.buffer, 0)
                table.insert(image.buffer, 0)
                table.insert(image.buffer, 0)
			end
		end
	end

    return image
end

-- dimensions of the generated texture
local WIDTH, HEIGHT = 400, 400

-- actually create the Mandelbrot texture
local tex = genMandelbrotTex(WIDTH, HEIGHT)
assert(#tex.buffer == 4 * WIDTH * HEIGHT, "invalid buffer length")

-- create an image texture node
texNode = octane.node.create{ type=octane.NT_TEX_IMAGE, name="Mandelbrot Texture" }
-- set up the gradient in the attributes
texNode:setAttribute(octane.A_BUFFER , tex.buffer , false)
texNode:setAttribute(octane.A_SIZE   , tex.size   , false)
texNode:setAttribute(octane.A_TYPE   , tex.type   , false)
-- evaluate the texture node
texNode:evaluate()