🚀 go-pugleaf

On the list FRAC-L <FRAC-L%GITVM1.BITNET@uga.cc.uga.edu> Fausto Barbuto
wrote:

>  Rio de Janeiro, BRAZIL, October 11, 1993:
>
>
> ====================================================
>              F I N A L   R E S U L T S
>  p-axis grid (NPIX) =       20000
>  q-axis grid (NPIY) =       10000
>  Iteration limit (ITERMAX) =   10000000.0000000000
>  Total number of points in the window =   200000000.000000000
>  Total number of points inside Mandelbrot =   53560708.0000000000
>  Ratio =  0.267803540000000007
>  Area of the window =   2.81250000000000000
>  --------------------------------------------------
>  MANDELBROT SET AREA =   1.50639491250000002
>  IN PERIODS 1, 2 =   1.43028393750000005
>  IN UNDECIDED =  0.325687499999999954E-04
>  DECIDED AREA =   1.50636234375000000
> ====================================================
>
> Period detection by Jay Hill, Mar/Apr 1993.
> Computer code by Fausto Barbuto & Jay Hill.
> System IBM Risc/600 Power 530H.
> Execution time: not computed.

Looks like a considerable execution time, Fausto, very impressive.

This is to be compared to the calculations of Fisher/Hill/Broadley
who obtained bounds on the area 1.5613027 from above and 1.5031197
from below. Also Robert Manufo calculated 1.50659530 +- 0.00000209
by averaging 40 runs with grids approximately 8192x4096.  Fausto's
result is about 95 standard deviations below Robert's result.

I hope we can settle this someday, since in theory exact areas of
components can be calculated.  The total through period eight is
1.48584014237616.  That is the sum of 236 components.  To get the
area to accuracy comparable to that claimed by pixel counters will 
require sums to beyond period 64, more than 18446744073709551616 
components ;-].  Of course most of these are ignoreable.  Since 
computing machines are increasing in speeds, doubling in speed every 
2 years, I should finish this sometime in 2034.  ;-)  Stay tuned.

Warmly, 
Jay 'Not tonight honey, I only need O(ln 2^n) more seconds' 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);}