radius = 10

-- create the pixel array
width = radius*2 + 1
height = radius*2 + 1
grid = {}

for i = 1, width do
    grid[i] = {}

    for j = 1, height do
        grid[i][j] = 0
    end
end

-- draw circle into grid
x0 = radius
y0 = radius

x = radius
y = 0
err = 1-x

while x >= y do
    grid[x+x0+1][y+y0+1] = 1
    grid[y+x0+1][x+y0+1] = 1
    grid[-x+x0+1][y+y0+1] = 1
    grid[-y+x0+1][x+y0+1] = 1
    grid[-x+x0+1][-y+y0+1] = 1
    grid[-y+x0+1][-x+y0+1] = 1
    grid[x+x0+1][-y+y0+1] = 1
    grid[y+x0+1][-x+y0+1] = 1
    y = y + 1

    if err < 0 then
        err = err + 2*y + 1
    else
        x = x - 1
        err = err + 2*(y-x+1)
    end
end

-- build turtle steps (1-indexed x, y from here on)
x = radius+1
y = 1
quarter = 1 -- top quarter, going around clockwise

forward = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}
left = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}
right = {{0, 1}, {-1, 0}, {0, -1}, {1, 0}}
change = {{1, 1}, {-1, 1}, {-1, -1}, {1, -1}}

function move(d)
    x = x + d[1]
    y = y + d[2]
end

while 1 do
    if x == radius and y == 1 then
        turtle.turnLeft()
        turtle.back()
        turtle.place()
        break
    end

    turtle.place()

    -- initial move
    move(forward[quarter])

    if grid[x][y] == 0 then
        if (quarter == 0 and (y > 0 and grid[x][y-1] ~= 0)) or
            (quarter == 1 and (x < width-1 and grid[x+1][y] ~= 0)) or
            (quarter == 2 and (y < height-1 and grid[x][y+1] ~= 0)) or
            (quarter == 3 and (x > 0 and grid[x-1][y] ~= 0)) then

            turtle.turnLeft()
            turtle.back()
            turtle.turnRight()

            move(left[quarter])

        elseif (quarter == 0 and grid[x][y+1] ~= 0) or
            (quarter == 1 and grid[x-1][y] ~= 0) or
            (quarter == 2 and grid[x][y-1] ~= 0) or
            (quarter == 3 and grid[x+1][y] ~= 0) then

            turtle.turnRight()
            turtle.back()
            turtle.turnLeft()

            move(right[quarter])
        end
    end

    turtle.back()

    if (quarter == 0 and width - x - 1 <= y) or
        (quarter == 1 and x <= y) or
        (quarter == 2 and x <= height - y - 1) or
        (quarter == 3 and x >= y) then

        turtle.place()
        turtle.turnRight()
        turtle.back()
        turtle.back()

        move(change[quarter])
        quarter = (quarter % 4) + 1
    end
end