Plotting the intersection of a composition function

My function is S:[0,1] ---> [0,1] I devide [0,1] into two parts [0,1/2), [1/2,1] and for each part I defined this:

For x in [0,1/2) , S(x)= x+1/4 (mod 1) and for x in [1/2 , 1), S(x)=x + 3/4 (mod 1).

I did this.

What I want is that how I can plot the intersection of S^k([0,1]) for k=1 till infinity ?

Answer 1

[Alan Stevens]

Do you mean something like this?

Sfn = @(x) (x+1/4).*(x<=1/2) + (x+3/4).*(x>1/2);
x = linspace(0,1,100);
n=10;
S = zeros(n,numel(x));
for k = 1:n
    
    S(k,:) = Sfn(x).^k;
    
end
subplot(1,2,1)
plot(x(1:50),S(:,1:50)),grid
axis([0 0.5 0 1])
subplot(1,2,2)
plot(x(51:end),S(:,51:end)),grid
axis([0.5 1 0 300])

[Torsten]

You forgot the "mod 1" in the equation for S.

[Reza Yaghmaeian]

I mean the INTERSECTION of S^k[0,1] for k=1 till infinity

[Torsten]

What is the "intersection of S^k[0,1] for k =1 to infinity" ?

The points that all S^k curves have in common ?

[Reza Yaghmaeian]

Yes exactly, but in mod 1

[Reza Yaghmaeian]

It's not a piecewise function too. You put sum between them