🚀 go-pugleaf

In article <1993Mar15.034914.12321@vms.eurokom.ie> David Doff writes:
>Consider the 1-dimensional M-set. It is instructive (and a lot faster) to
>compute the length of the 1-D M-set. Of course, by inspection, the length
>is 2.25. However, if you do it by pixel counting, the length converges to
>a value close to 1.70 as the value of imag(c) tends to zero.

>This makes sense, if you think of the left hand part of the real line as
>a Cantor-like set. This also indicates that the regions of Chaos occupy
>a total length of about 0.55 and only this amount of the real line is
>infinitely thin.

I still have not seen an answer to: What portion of the real line has 
periodic orbits vs. chaotic.  The periodic parts are in the cardioids and 
buds.  Since we know the Feigenbaum point is -1.401155, from 0.25 to 
-1.401155, 1.651155 is definately periodic.  So an upper bound of .598845 
is infinitely thin or 26.7% of (-2 to 0.25).

Is there a known result?  Is the chaotic length definitely greater than 0?

Warmly,
Jay 'Not tonight honey, I'm looking for a real chaotic point' 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);}