Identify this plant - Portulaca grandiflora

I was traveling in Taichung recently and saw these plants near Nina's Chocolate Factory 妮娜巧克力工坊. They were beautiful and I couldn't resist plucking one each. One is purple and the other is white. I didn't know whether they will survive one week in my luggage when I'm having vacation in Taiwan. The plants did survive and now have grown much bigger. However, the white flower plant didn't manage to branch out. I do not know whether it will in the future. The purple flower plant has a few branches now and I'm going to cut one branch and propagate it into another plant in one week or so. I will update again.

Purple flower plant - 3 branches

White flower plant - no branch

Update: This plant is Portulaca grandiflora or Moss Rose.