They're fairly easy to acquire if you know what you're doing.
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Apparently I don't know what I'm doing. I was on patrols on morning for 3 hours and never saw a public event today.
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http://destinypublicevents.com
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Maybe I worded that wrong. But if you're on Xbox 360, I'm willing to help. If not, the Daily Heroic stories. Lv 26 gives 1 ascendant material, Lv28 gives 2. Be sure purchase faction gear and weapons as well. And the weekly strike has a chance to drop either 10 or 11 ascendant shards, energy or strange coins. And for 3 characters, this is a lot easier. I had the luck of getting 11 ascendant shards and 11 ascendant energy from the weekly strike back to back.
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You can go online and search for public event timers. Some may not appear but it's better than doing nothing.
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Always do the strikes on the lowest level. That must be my problem.