[Scilab-users] Visualising Collatz sequences

[Stéphane Mottelet]

You can also enjoy the 3d version:

function  X=anglePath3(r, th, ph)
     cumth  =  cumsum(th);
     cumph  =  cumsum(ph);
     X  =  cumsum([0  r.*sin(cumph)
                 0  r.*sin(cumth).*cos(cumph)
                 0  r.*cos(cumth).*cos(cumph)],  2);
end

function  N=collatz(n)
     N  =  n;
     while  n<>1
         if  modulo(n,2)  ==  0
             n  =  n/2;
         else
             n  =  3*n+1;
         end
         N  =  [n  N];
     end
end

a=0.1;
e=1.3;

clf
NCOL=512;
gcf().color_map=parulacolormap(NCOL);
drawlater
for  i=1:200
     r=collatz(grand(1,1,'uin',1,1000000));
     m1=modulo(r,4);
     m2=m1;
     m1(m1>1)=0;
     m2(m2<=1)=0;
     X=anglePath3(r./(1+r.^e),a*%pi*(0.352-modulo(m1,2)),a*%pi*(0.352-modulo(m2,2)));
     x=rand(3,1)/8;
     param3d(x(1)+X(1,:),x(2)+X(2,:),x(3)+2*X(3,:))
     gce().foreground=min(NCOL,length(r))
end
isoview  on
drawnow


Le 14/04/2022 à 09:46, Stéphane Mottelet a écrit :
>
> Hi again,
>
> Here is a small code doing the graphic job:
>
> function  X=anglePath(r, th)
>      cumth  =  cumsum(th);
>      X  =  cumsum([0  r.*cos(cumth);0  r.*sin(cumth)],  2);
> end
>
> function  N=collatz(n)
>      N  =  n;
>      while  n<>1
>          if  modulo(n,2)  ==  0
>              n  =  n/2;
>          else
>              n  =  3*n+1;
>          end
>          N  =  [n  N];
>      end
> end
>
> a=0.08;
> e=1.2;
>
> clf
> gcf().color_map=graycolormap(128);
> for  i=1:100
>      r=collatz(ceil(rand()*2000000000));
>      X=anglePath(r./(1+r.^1.2),a*%pi*(0.35-modulo(r,2)));
>      plot(0.01+X(1,:),-0.01+X(2,:));
> end
> -- 
> Stéphane Mottelet
> Ingénieur de recherche
> EA 4297 Transformations Intégrées de la Matière Renouvelable
> Département Génie des Procédés Industriels
> Sorbonne Universités - Université de Technologie de Compiègne
> CS 60319, 60203 Compiègne cedex
> Tel : +33(0)344234688
> http://www.utc.fr/~mottelet
>
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-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet
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