Jane has successfully named this plant the Rainbow Gum Tree (that's Eucalyptus Deglupta to you). According to Wikipedia, this is the only eucalyptus tree native to the northern hemisphere. It is most commonly grown for pulp wood in making paper and for ornamental purposes.
"This tree is also grown for ornamental purposes, due to the showy multi-coloured streaks that cover the trunk. Patches of outer bark are shed annually at different times, showing the bright-green inner bark. This then darkens and matures to give blue, purple, orange and then maroon tones"I had no idea such a tree existed. Cale and I were walking around in the national park up the mountain from Chiang Mai, when we happened to turn the corner and stumble on this tree. At first we thought it had been painted, until we realized that they were everywhere and all the trees were equally colorful. Cale describes them as Picasso trees. They are my new favourite plant.