A321 pilot flying reported a track deviation occurred while climbing out of LAX when the flight crew were distracted by a wake turbulence encounter.

Narrative

During taxi out in LAX from Gate XX; we were assigned Runway 24L. This is not the normal route nor runway for us out of LAX so we briefed the new taxi route and proceeded to change the runway and verify the SID procedure as we taxied to 24L. We both verified in the Multipurpose Control Display Unit (MCDU) that the runway and SID were correct as well as the appropriate performance data for Runway 24L. There were no discontinuities and all altitudes restrictions were in place. We then departed behind a heavy Aircraft Y. Upon initial climb out; we twice encountered substantial wake turbulence from the preceding aircraft and my attention was mostly drawn to controlling the aircraft. We were given climb via the SID" from Departure Control and I set 14;000 feet managed in the altitude select window. Reviewing our data and our memories of the situation; both the FO and I are very confident that we were flying the proper SID and transition. The data shows we started our left turn at approximately 10 NM after departure which agrees with the ZILLI5.FICKY transition. While in this turn; ATC told us to stop climb at 6;000 feet and turn right to 250 heading for traffic. It appeared to us that a departure off 25R was off to our left as we turned on the SID. As I stated; we were both in managed NAV and CLIMB when we started the turn.I believe due to the wake turbulence; my attention was diverted from our flight path. I was focused on maintaining control and did not give my usual attention to what was our next fix and altitude restriction. Runway changes are never a welcome thing. I also feel that I could have spent more time on a route verification after the runway change was complete. I looked it over quickly but did not give it my normal thoroughness."