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Yeah, it was made as an April fool joke by a science writer a while back. The first time I read it, it really had me, I have to admit. It seemed feasible:

120x120 is 14400 pixels. In a 3x3-sized area in the complex number plane centered on (0,0), with a max count of 70, the average number of iterations is about 30. That's about 430,000 iterations all together.

If you spent 9 years doing this 16 hours per day, 6 days a week (I assume Sunday would have been off-limits), you'd have to do about 9.6 iterations per hour. Each iteration is only three multiplications and three additions (one of which is really a x2), so this might just be possible if you have a few highly dedicated friends helping.