One of the hardest things can be getting started. Belinda Spiwak has a nice tutorial on her blog, and this video of a Mandela Zentangle will definitely make you want to give this a try.
Now for a few Zentangles of my own. Although there appears to be variation in their color, these were all done on the same basic white paper. The sunlight was definitely playing tricks on me today when I was trying to take pictures.
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Now that you've seen how easy this is, grab that paper and pen that you already have on hand and make some marks!