Identification of Flower and Plant

Got this plant from Taiwan when I was having a holiday there in October. Can anyone help to identify this plant and flower's name? Thanks in advance.

There are two types of this plant. One gives purple flower and the other gives white flower. They are gorgeous looking and I try to cross pollinate them to see whether they give any seeds. I saw another type in my friend's garden in Malaysia which gives white and purple coloured patches in a single flower. I was thinking whether this was caused by the cross-pollination of the purple and white flowers. Anyway, I will ask my friend to pass me a single stalk so that I can grow them.

Purple & white flower

This plant is very easy to grow. You just need to pluck a stalk (stem) with leaves on it. Place the stem into a cup of water and you can see the roots coming out very quickly. In a few days, you will see many roots coming out from the end of the stem. Once the roots have been established, you can plant them into the soil.

I notice that this plant likes to be in the sunny place. The leaves will open widely under the sun. When night falls, the leaves will fold up in a closed position.

The flower will only bloom for one day. So, when it blooms, quickly enjoy the flower and then at night the flower will collapse. But a new bud will grow quickly and the flower will bloom again in a week or so.

What is the name of this plant/flower?

The white version, what is this plant's name?

Drop me an email or comment. Thanks.