🚀 go-pugleaf

In article <1993Sep15.194315.6575@ast.saic.com>, hilljr@jupiter..saic.com (Jay R. Hill) writes:
|>             Universal constant not universal?
|> 
|> The 'Universal' constant, whose value was first reported in 1977 by
|> Grossmann and Thomae and which was found by Feigenbaum to be in many 
|> nonlinear processes, seems to change with each new publication 
|> appearance!
|> 
|> It takes on at least three different values in the first 3 books
|> I found it in.
|> 
|> In 1986 Peitgen and Richter report the value on page 7 of The Beauty
|> of Fractals as 4.669201660910...
|>                         ^

And let me quote the FAQ.

>Subject: Feigenbaum's constant

>Q10: What is Feigenbaum's constant?
>A10: In a period doubling cascade, consider the parameter values where
>period-doubling events occur.  The limit of the ratio of distances between
>consecutive doubling values is Feigenbaum's constant.  It has the value
>4.669201660910...
          ^
|> The 1990 edition of Dynamical Systems and Fractals by Becker and
|> Dorfler (p48) puts delta = 4.669201660910299097...
|>                                     ^        ^^
|> But in 1992 Peitgen, Jurgens and Saupe's Chaos and Fractals New
|> Frontiers of Science, page 612, list the delta at 4.6692016091029...
|>                                                           ^      ^^
|> I have calculated it and submit for your consideration for 1993 this
|> value for delta: 4.66920160910299067197...        ;-)
                    4.66920160910299067185...
Another day has passed, so I now claim it is more like the update.
|> 
|> BTW I get -1.40115518909205060052382678789... for the Mandelbrot Set
Make this    -1.4011551890920506005238267878939...
|> Feigenbaum point.
|> 
|> Warmly,
|> Jay 'Not tonight honey, I'm changing the Universal Constant' Hill
|> -- 

Now I cross-post sci.fractals and bit.listserv.frac-l.  From frac-l:

> Date:         Thu, 16 Sep 1993 09:35:29 CDT
> From: Dave Uherka <UHERKA%NDSUVM1.BITNET@uga.cc.uga.edu>
> Organization: North Dakota Higher Education Computer Network
> Jay:  Do you think the first two values that you quoted for the
> "feigenbaum" number just had typos where the second "66" occurred?
>      Also, how did you calculate your value so accurately and how
> long did it take?
> .....Dave Uherka, Math Dept, U of ND

'typos' - fine, but who is to know.  Do I stack up the books plus
the FAQ, for a vote, or use my number.  :-)  The typo is being
spread throughtout the literature.  I in fact used it to extrapolate
my 1-D chaos vs periodic length calculation, producing an inaccurate
result!  Besides, computing it is fun, especially when the books
don't agree!  ;-)

How did I calculate it?  Well I coded up Newton's method in C++ 
multiprecision and let er rip.  I solve for the successive component 
centers along the period doubling sequence.  Up to period 2^25 now.  
More than 2 days on my 486/33.  Ticked off my 12 yr old son who 
wanted to play XWING.  

-- Jay 'Not tonight honey, just two more digits, just two more' Hill
{ hilljr@jupiter.saic.com } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}