Re: [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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users mailing list
users@lists.scilab.org
http://lists.scilab.org/mailman/listinfo/users