This image show relation between distance to landing point and escape time of given point of external ray.
There are points of 2 rays ( both have external angle t = 1/3 and land on point of period 2 parabolic cycle) :
* parabolic ray ( c = -3/4 ) which lands on z = -0.5
* superattracting (non-hyperbolic) ray ( c = 0 ) which lands on z = e^(2*i*Pi*t) = 0.86602540378444*%i-0.5



In parabolic case next (estimated) values are :
distance ; escape time
0.05 ; 200
0.04 ; 300
0.03 ; 500
0.02 ; 1000

In case when pixel width is 0.004 it means that after 1000 iterations ray is still 5 pixels from its landing point (:-|