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 (:-|