local Complex={type="package"}

local function complex(x,y)
 return setmetatable({ re=x, im=y }, Complex.metatable)
end

function Complex.conj(x,y)
 return complex(x.re,-x.im)
end

function Complex.norm2(x)
 local n=Complex.mul(x,Complex.conj(x))
 return n.re
end

function Complex.abs(x)
 return sqrt(Complex.norm2(x))
end

function Complex.add(x,y)
 return complex(x.re+y.re,x.im+y.im)
end

function Complex.mul(x,y)
 return complex(x.re*y.re-x.im*y.im,x.re*y.im+x.im*y.re)
end

Complex.metatable={
	__add = Complex.add,
	__mul = Complex.mul,
}

local function abs(x)
 return math.sqrt(Complex.norm2(x))
end

xmin=-2.0	xmax=2.0	ymin=-2.0	ymax=2.0
N=arg[1] or 256 

function level(x,y)
 local c=complex(x,y)
 local l=0
 local z=c
 repeat
  z=z*z+c
  l=l+1
 until abs(z)>2.0 or l>255
 return l-1
end

dx=(xmax-xmin)/N
dy=(ymax-ymin)/N

print("P2")
print("# mandelbrot set",xmin,xmax,ymin,ymax,N)
print(N,N,255)
local S = 0
for i=1,N do
 local x=xmin+(i-1)*dx
 for j=1,N do
  local y=ymin+(j-1)*dy
  S = S + level(x,y)
 end
 -- if i % 10 == 0 then print(collectgarbage"count") end
end
print(S)