NMAC IN GA TFC PATTERN.

Narrative

ON TKOF ROLL; TWR REQUESTED AN IMMEDIATE HARD R TURN AND BEST RATE OF CLB TO AVOID CONFLICT WITH ANOTHER ACFT ALSO TURNING R; HAVING JUST DEPARTED ON THE PARALLEL RWY 31L. I WAS DEPARTING ON RWY 31R; BEHIND THE OTHER ACFT. AFTER LIFT-OFF; WITH THE OTHER DEPARTING ACFT IN SIGHT; I BECAME UNSURE AS TO WHEN TO MAKE MY R TURN; SINCE A SIGN AT THE TXWY ENTRANCE TO RWY 31R SPECIFIED NO TURNS BEFORE REACHING 600 FT; DUE TO THE HIGH HILL ON THE NE SIDE OF THE ARPT. I MADE BEST RATE OF CLB TO 600 FT AND MADE AN IMMEDIATE R TURN. HOWEVER; SHORTLY BEFORE I REACHED 600 FT THE BFI TWR TOLD THE OTHER ACFT THAT I HAD HIM IN SIGHT; I WOULD BE TURNING IMMEDIATELY AFTER DEP AND THAT HE COULD START HIS R TURN. THE OTHER ACFT'S TURN 'EARLY' COMBINED WITH MY TURN ONLY AFTER REACHING 600 FT CAUSED US TO CONVERGE RAPIDLY. I WAS OVERTAKING AND CONVERGING AND CHOSE TO FLY BEHIND AND TO THE L OF THE OTHER ACFT. AS WE CONVERGED; I STAYED BELOW THE OTHER ACFT (A HIGH WING CESSNA) SO THAT WE COULD SEE ONE ANOTHER. I THOUGHT WE WERE GOING TO CLR BY A WIDE MARGIN AS I OVERTOOK AND AS THE OTHER ACFT CONTINUED HIS R TURN. BUT THE OTHER ACFT STOPPED TURNING R; MAY HAVE TURNED SLIGHTLY L AS I BEGAN TO PASS ON HIS L. I ALTERED COURSE FURTHER L TO WIDEN OUR MARGIN OF CLRNC; BUT MY CORRECTION WAS INADEQUATE TO WIDEN OUR SEPARATION ADEQUATELY (IN LIGHT OF WHAT I BELIEVE WAS HIS CONTINUING L TURN; PROBABLY BROUGHT ON BY NOT KNOWING MY EXACT POS BELOW AND BEHIND HIM). AS WE CAME PARALLEL TO ONE ANOTHER; WE BOTH EXECUTED TURNS IN OPPOSITE DIRECTIONS; HIM R; ME L TO KEEP CLR. PRIOR TO EXECUTING MY DECISION ON CLB OUT TO STAY L (BEHIND) AND BELOW THE OTHER DEPARTING ACFT; I BROADCAST ON THE TWR FREQ THAT I WOULD TURN N (AND L) OF THE OTHER DEPARTING ACFT AS HE CONTINUED HIS R TURN. THIS WOULD KEEP ME BEHIND THE OTHER ACFT. I RECEIVED NO RESPONSE FROM THE TWR OR THE OTHER ACFT. AT NO TIME WAS THE OTHER ACFT OUT OF MY SIGHT. WE KEPT THE OTHER ACFT IN SIGHT UNTIL WELL CLR AHEAD BEFORE CLBING ABOVE 1200 FT MSL. IN RETROSPECT; I SHOULD HAVE TURNED PRIOR TO REACHING 600 FT; OR AT LEAST ASKED THE TWR FREQ FOR CLARIFICATION OF ITS INSTRUCTIONS IN THAT REGARD. IN ADDITION; I PROBABLY SHOULD HAVE TIGHTENED MY TURN TO THE R INSTEAD OF CHOOSING TO PROCEED BEHIND THE OTHER ACFT AS I OVERTOOK IT; THIS WOULD HAVE KEPT US CLRER OF ONE ANOTHER. HOWEVER; TURNING INTO WHAT APPEARED TO BE THE PATH OF THE OTHER R-TURNING ACFT WAS REPUGNANT TO ME AT THE TIME. IN ADDITION; BY PROCEEDING FURTHER R; I FEARED AT THE TIME; I MIGHT FIND MYSELF IN CONFLICT WITH THE RENTON ARPT CTL ZONE IN SHORT ORDER.