Using complex numbers:

    z = 0;
    c = input_from_user();
    for (int i=0; i<1000; i+=1)
      z = z*z+c;

for any givel value of c does the repeated
computation diverge (shoot off towards infinity)
or remain a prisoner of the "small numbers" region?

Here are some of the more interesting values for
c for test cases:

     real  imaginary
    -----------------
     1.0    0.0    
     0.9    0.1   both get infinite very quickly

     0.3    0.315   the remander give interesting shapes
     0.355  0.295
    -0.26  -0.625
    -0.49   0.56
     0.025 -0.65
     0.43  -0.255
     0.375 -0.255