I am revising the unstable period orbits of the Logistic map, y[n]=4*y[n-1]*(1-y[n]), in Maple. Although I have implemented the equation and use a loop for the iterations, I wonder whether there is a faster and concise way to code the equation in Maple.
Here it is what I did:
y := (-sqrt(5)+5)*(1/8);
for n to 10 do y[n] := 4*y[n-1]*(1-y[n-1]) end do;
soly := [seq(simplify(expand(y[n]), radical), n = 0 .. 10)];
dat := [seq([n, Re(evalf(soly[n]))], n = 1 .. 10)]; plot(dat, labels = ["k", "x(k)"], style = pointline,title="Period 2");
Since only few iterations are needed, the solution is symbolic (and then convert to float).