Python 3

Translation from perl (193) with some improvements

185 chars

Y=-1.2
r=range
for _ in r(25):
 X=-2
 for _ in r(80):
  r=i=0
  for n in r(16):
   r,i=r*r-i*i+X,2*r*i+Y
   if r*r+i*i>4:break
  print(".,:;=+itIYVXRBM "[n],end='')
  X+=3/80
 Y+=2.4/25

Python 3, 185 bytes

Translation from perl (193) with some improvements

Y=-1.2
r=range
for _ in r(25):
 X=-2
 for _ in r(80):
  r=i=0
  for n in r(16):
   r,i=r*r-i*i+X,2*r*i+Y
   if r*r+i*i>4:break
  print(".,:;=+itIYVXRBM "[n],end='')
  X+=3/80
 Y+=2.4/25