Plotting the intersection of a composition function

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Reza Yaghmaeian 2021-5-30

评论： Reza Yaghmaeian 2021-5-30

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 ?

Alan Stevens 2021-5-30

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])

Reza Yaghmaeian 2021-5-30

Yes exactly, but in mod 1

Reza Yaghmaeian 2021-5-30

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

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