from multiprocessing import Pool

def escapes(cr, ci, it):
    """
    Does iterating z <- z^2 + c escape after it iterations?

    Pure function.
    """
    zr = 0.0
    zi = 0.0
    for i in xrange(it):
        # z <- z^2 + c
        zr,zi = zr*zr - zi*zi + cr, 2*zr*zi + ci
        if zr*zr + zi*zi > 4:
            return True
    return False

def toChar(p):
    if p:
        return " "
    else:
        return "X"

def doRow((xmin,xmax,xstep, ymin,ymax,ystep, iterations, yc)):
    """
    Calculate one row of the output.
    
    Pure function.
    """
    y = yc*(ymax-ymin)/ystep + ymin
    row = []
    for xc in xrange(xstep):
        x = xc*(xmax-xmin)/xstep + xmin
        row.append( escapes(x, y, iterations) )

    return "".join([toChar(p) for p in row])

def mandel(xmin,xmax,xstep, ymin,ymax,ystep, iterations):
    """
    Calculate and print a Mandelbrot set.
    """
    pool = Pool()
    
    args = [(xmin,xmax,xstep, ymin,ymax,ystep, iterations, yc) for yc in xrange(ystep)]
    #rows = pool.map(doRow, args, chunksize=1)
    rows = map(doRow, args) # serial version
    print "\n".join(rows)

def mandelX(xmin,xmax,xstep, ymin,ymax,ystep, iterations):
    """
    Calculate and print a Mandelbrot set.
    
    (Alternate implementation that prints each row as it is calculated.)
    """
    pool = Pool()
    results = []
    for yc in xrange(ystep):
        res = pool.apply_async(doRow, ((xmin,xmax,xstep, ymin,ymax,ystep, iterations, yc),))
        results.append(res)

    for yc in xrange(ystep):
        print results[yc].get()

if __name__=="__main__":
    mandel(-2.0, 1.0, 100, -1.0, 1.0, 60, 20000)