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Jonathan Coulton – Mandelbrot Set Lyrics 16 years ago
Kiro5505 is correct. The Mandelbrot definition has C as the point in the complex plane, not Z. Z starts at zero. JoCo could have written it this way:

Take a point called C in the complex plane
Let Z1 be C squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to zero and never trends away
That point is in the Mandelbrot Set

That isn't the traditional way of defining the set, but it's equivalent. It obviates the need to mention that Z starts at zero. It also offsets the usual subscript values by one, but since it's the end result of an infinite series that matters, which subscript is which is irrelevant. The meter scheme of JoCo's song is preserved.

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