For the discrete dynamical system: x(t+1) = x(t)^2 + c with x(0)=0. Evaluate the
ID: 2902759 • Letter: F
Question
For the discrete dynamical system: x(t+1) = x(t)^2 + c with x(0)=0. Evaluate the system for values of c=a+b*i in the complex plane for a and b in the interval [-1.5,1] with interval size of 0.005 (hint: build c in matrix form using meshgrid). Evolve the system up to t=20 for all values of c in parallel. Use image() to display, in the complex plane, those values of c for which |x(20)| < 2.
Looking for the steps on being able to write this out and view the image in MATLAB
Prefer the code now, and it should be able to run without any need to change it.
Explanation / Answer
clear ; clc;
x[0]=0;
a=-1.5:0.005:1;
b=-1.5:0.005:1;
%c=a+b*i
c= [X,Y] = meshgrid(a,b);
for i=1:size(X)
for j=1:size(Y)
for t =0:20
x[t+1] = x[t]^2 +c(i,j) ;
end
end
end
zx= freqz(x);
figure,imshow(zx);
figure, imshow(x);