Re: fun with Collatz

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2021-12-29 03:35, Ruud H.G. van Tol wrote:
> \\ 4-dimensional approach ;)
>
> im_run1( RI= 23 )=
> {
>    my
>    ( v0=  RI
>    , v0r= real(v0)
>    , v0i= imag(v0)
>    , p2=  if(frac(v0r), 1/frac(v0r), if(v0i,1,0)) \\ halving counter
>    , p3=  if(frac(v0i), 1/frac(v0i), if(v0i,1,0)) \\ tripling counter
>    , c2=  if( v0i, floor(v0i), floor(v0r) )
>    );
>
>    c2/= 2^valuation(c2, 2);  \\ oddify
>
>    my
>    ( c3= c2 \\ (p2*x + c2) -> (p3*x + c3)
>    , n=  (c2 - 1) / 2
>    );
>    if( !n, c2= p2= p3= 0; c3= 1 );
>
>    while
>    ( (c3 > 1) && (c3 >= c2) \\ stop-condition
>    , c3= 3 * c3 + 1;
>      p3++;
>      while
>      ( 0 == (c3 % 2)
>      , c3/= 2;
>        p2++;
>        if(c3 < c2, break); \\ dropper
>      );
>    );
>
>    (c2 + if(p2>1,1/p2,0)) + I * (c3 + if(p3>1,1/p3,0));
> };

Example usage:

{
my
( v= 9781262575275081247
, w= 1+floor(log(v)/log(10)) \\ digits
);
while
( real(v) > 1
, my(vr=real(v), vi=imag(v), p2=frac(vr), c2=floor(if(vi,vi,vr)));
  p2= if(p2, 1/p2, 0);
  printf("> %*s  2^%s\n", w, c2, p2);
  v=im_run1(v);
)
}

-- Ruud