%% Diagramme de Verhulst
%% -----------------------------------------
%% Jean-Michel Sarlat (12 janvier 2002)

color couleur[]; 
 
vardef verhulst(expr rmin, rmax, ur, ux) = 
 r := rmin; 
 pr := (rmax - rmin)/250 ; 
 for i = 1 upto 250: 
    x := .3; 
    for j=1 upto 100: 
        x := (1+r)*x-r*x*x; 
    endfor 
    for j=1 upto 200: 
        x := (1+r)*x-r*x*x; 
        draw (r,x) xscaled ur yscaled ux 
            withpen pensquare scaled 1pt 
            withcolor (i/200)[couleur1,couleur2]; 
    endfor 
    r := r +pr; 
 endfor; 
enddef;


beginfig(1);
    couleur1 = (.8,.2,.4); 
    couleur2 = (.2,.6,.8); 
    verhulst(1.9,3,10cm,6cm);
endfig;

end