🚀 go-pugleaf

In article <C4E0vu.7Gy@world.std.com>, mrob@world.std.com (Robert P Munafo) writes:
|> It has been a little over a week since I announced that I would coordinate a
|> second GIPPP to estimate the area of the Mandelbrot Set.  Here's what has
|> happened since then:
|>  
|> * I have received responses from quite a few people, representing a combined
|> computing resource that is sufficient to take on the amount of work that I
|> am planning on trying to do.

I don't know how many pieces you are going to cut M into, but here are some
numbers.  If we cut the region into a 16x16 (-2,0)-(0.5,1.125) I figure
we have about 70 edge zones which need pixel counting. The others are all out
or all in.   If its 32x32 we must do about 400. And 64x64 is about 1000 runs.

|>  
|> * Jay Hill has advised me to consider using a very high dwell limit, on the
|> order of 8388608 or 16777216, inasmuch as the error due to sampling seems
|> to be significantly lower than the error due to the dwell limits that I was
|> originally planning to use.  

I used 8192 x  4096 @ 8987185 for nx,ny,iter and got 1.506594 for the in
M-Set area with less than 73 pixels unable to decide to exit or converge
to a specific period.  That is 73 out of nearly 9M.  The deep iteration
limit tightens up the uncertainty of pixel counting area estimates.

|>I am currently running a series of area estimates on ten grids ...

|> running.  It appears now that the 131072x65536 size is the one I'll pick; I

That is only 4 times what you posted last time. You were using 4 Sparks at
say 48 hours each.  Now we have about 32 days of Spark time to do this.
Should not be too bad.

|>  ...
|> mrob's .sig #2 

Warmly,
Jay
-- 
{ 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<3;n++);
printf("%17.15lf\n",1/a);}