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A relationship between Pi and the Mandelbrot set. a(n) = number of iterations of z^2 + c that c-values -.75 + x*i go through before escaping, where x = 10^(-n). lim n->inf a(n) * x = Pi.

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3, 33, 315, 3143, 31417, 314160, 3141593, 31415928 (list; graph; listen)

	OFFSET	`0,1`
	COMMENT	`-.75 + 0*i is the neck of the Mandelbrot set`
	REFERENCES	`Peitgen, Juergens and Saupe: Chaos and Fractals (Springer-Verlag 1992) pages 859-862` `Peitgen, Juergens and Saupe: Fractals for the Classroom (Springer-Verlag 1992) Part two, pages 431-434`
	LINKS	`Dave Boll Pi and the Mandelbrot set` `Boris Gourevitch Pi et les fractales Ensemble de Mandelbrot - Dave Boll - Gerald Edgar (entrez Mandelbrot et appuyez sur le bouton "Sur ce site")` `Aaron Klebanoff Pi in the Mandelbrot set (proof)`
	CROSSREFS	`Sequence in context: A043038 A107127 A135697 this_sequence A121515 A002277 A001507` `Adjacent sequences: A097483 A097484 A097485 this_sequence A097487 A097488 A097489`
	KEYWORD	`nonn`
	AUTHOR	`Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 19 2004`

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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.

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