A C172 PLT AT TNN FAILED TO FOLLOW ATC POST TKOF HDG INSTRUCTIONS AND HAD A NEAR MISS WITH ANOTHER ACFT IN THE PATTERN.

Narrative

UPON INITIAL DEP FROM TTN; I MISSED AN INSTRUCTION FROM THE TWR CTLR TO MAINTAIN RWY HDG ON CLBOUT. A C206 HAD DEPARTED IMMEDIATELY BEFORE ME; AND WAS TO REMAIN IN THE ARPT TFC PATTERN. AS I CLBED TO ALT; I HAD THE C206 IN SIGHT; AT 1200 FT MSL I TURNED S TO DEPART TTN AIRSPACE; WITH THE C206 OFF OF MY 1 O'CLOCK POS; UNAWARE OF HIS INTENTIONS. THE TWR CTLR ASKED ME IF I HAD TFC AT 3 O'CLOCK POS; TO WHICH I REPLIED NEGATIVE; NOT REALIZING THAT THE CTLR WAS REFERRING TO THE C206. THE TWR CTLR THEN CLRED THE C206 TO DOWNWIND; WHILE I CLBED TO 1500 FT MSL. I HAD TO CLB TO AVOID A DANGEROUS SITUATION WITH THE C206. AS IT PASSED UNDER ME; THE CTLR ASKED IF I HAD THE TFC; TO WHICH I REPLIED 'I DID AS HE PASSED UNDERNEATH ME.' THE CTLR THEN SAID I HAD IGNORED TFC RPTS AND THAT I HAD IGNORED AN ASSIGNMENT TO REMAIN ON RWY HDG. I DO NOT RECALL HEARING ATC TELLING ME TO REMAIN RWY HDG; AND ATC GAVE ME A TFC UPDATE ONCE. UPON REACHING TTN AT THE CONCLUSION OF THE FLT; I WAS INSTRUCTED TO CALL THE TWR WHEN SHUTDOWN; WHICH I DID. THE CTLR THAT ANSWERED THE TELEPHONE RELAYED A MESSAGE TO ME FROM THE TWR CTLR THAT WORKED ME ON TKOF TO PAY ATTN TO ATC INSTRUCTIONS. THE CAUSE OF THIS INCIDENT WAS ME NOT HEARING THE TWR CTLR ISSUE ME A HDG; WHICH CAUSED A POTENTIALLY HAZARDOUS SITUATION THAT COULD HAVE RESULTED IN AN AIRBORNE COLLISION.