Haskell, 175 bytes
t=take 16
f=t0ドル:f
p s(a:b)=s%(a:a:b)
s%(a:b:c:d)=s(4*a+2*b+c):s%(b:c:d)
s%[a,b]=[s6ドル*a+b]
n=putStrLn
m s=n"P3 33 16 1">>mapM_((n"0 0">>).print)`mapM_`t(iterate(p(s!!))$f++1:f)
Outputs to a ppm file with blue being on and black being off. You can adjust the colors somewhat but blue is the golfiest of the primary colors.
Sample outputs
Rule 30
Raw
Increased size
Rule 121
Raw
Increased Size
Wheat Wizard ♦
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