funny thing that JoCo hapens to know about his own song, that if you ask a mathematician/physisist the song does explain a set, just not the Mandelbrot Set
Pretty sure this does describe the Mandelbrot Set. I mean, sure the better way to put it would state that the magnitude of Z remains < 2, but the way the lyrics are written is correct, just not quite as concrete. And I mean "If the series of Z's should always stay/Close to Z and never trend away": Catchy. And "If the magnitude of the series of Z's remains/less than 2 and never diverges": kinda lacking.
Pretty sure this does describe the Mandelbrot Set. I mean, sure the better way to put it would state that the magnitude of Z remains < 2, but the way the lyrics are written is correct, just not quite as concrete. And I mean "If the series of Z's should always stay/Close to Z and never trend away": Catchy. And "If the magnitude of the series of Z's remains/less than 2 and never diverges": kinda lacking.
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:
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
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...
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.
funny thing that JoCo hapens to know about his own song, that if you ask a mathematician/physisist the song does explain a set, just not the Mandelbrot Set
Pretty sure this does describe the Mandelbrot Set. I mean, sure the better way to put it would state that the magnitude of Z remains < 2, but the way the lyrics are written is correct, just not quite as concrete. And I mean "If the series of Z's should always stay/Close to Z and never trend away": Catchy. And "If the magnitude of the series of Z's remains/less than 2 and never diverges": kinda lacking.
Pretty sure this does describe the Mandelbrot Set. I mean, sure the better way to put it would state that the magnitude of Z remains < 2, but the way the lyrics are written is correct, just not quite as concrete. And I mean "If the series of Z's should always stay/Close to Z and never trend away": Catchy. And "If the magnitude of the series of Z's remains/less than 2 and never diverges": kinda lacking.
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:
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
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...
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.