Pilot reported they were unsure of which heading to fly during departure in IMC and flew into an area below the minimum IFR vectoring altitude.

Narrative

Departing ZZZ to Location at ZZZ1 yesterday (Day) the Tower Controller issued a new heading after we had begun our taxi. As a single pilot I elected not to stop and write the new clearance down and instead bugged the new heading and read it back; receiving no further comment. I honestly do not recall if the new clearance included which direction to turn or; if so; if I read it back. In any case on departure I made a turn to the west instead of the east turn which the controller expected and which would have been indicated by the traffic pattern. I was well above pattern altitude when I began my turn. At no time was I in IMC and there was no conflicting traffic but the Departure Controller asked me to call the tower when I landed; which I did. The controller I had the issue with was off shift by the time I landed and the gentleman I spoke with explained that by turning west I had flown into an area while below the minimum IFR vectoring altitude for that segment. Today on an identical departure from ZZZ to ZZZ1 the controller issued me the same heading but he specified 'cleared via radar vectors' and specified the left (east) turn.