CobWeb Plot em Octave

Descrição

Esconder código-fonte

#########################################################################################
#####                                                                                                                                                              #####
#####              Gráfico CobWeb da função quadrática f(x) = x²+l                                                                 #####  
#####                                                                                                                                                              #####
#########################################################################################


function [u,v] = chaos(x0, l, n)

# x0 = ponto inicial, isto é, f^0(x0);
# l = parâmetro da função quadrática;
# n = número de iterações;

k=2*n;

x= zeros(1,k+1);
y=zeros(1,k+1);

x(1)=x0;
y(1)=0;

   for i=2:k;
      if (rem (i, 2) == 0) #i é par
      x(i) = x(i-1);
      y(i) = x(i-1).*x(i-1)+l;
      else #i é ímpar
      x(i) = y(i-1);
      y(i) = y(i-1);
      endif
   end

 p=((1+sqrt(1-4*l))./2);

 u=-p:0.01:p;      # p=((1+sqrt(1-4*l))./2) é o maior ponto fixo.
 v=u.*u +l;        # note que precisamos ter \delta = 1 - 4*l > 0  

plot(x,y,u,v,u,u)


endfunction