R, 141 bytes

r=i=1:396/99-2 s=sapply image(s(i,function(x)s(r,function(y){ n=z=0;c=complex(i=x,r=y) while(n<=99&abs(z)<2){z=z*z+c;n=n+1} n })),c=colors()) 

6y after the Q was asked, but I love Mandelbrot sets, and the earlier R solution was 211 characters...