[Scilab-users] Visualising Collatz sequences

[Stéphane Mottelet]

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 collatz

-- 
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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