 # Matlab Code for Tent Map and Histograms of Chaos Sequences

## Question

1: write the matlab code for tent map: Let 0<b<=1. Let f(x)=bx for x<1/2 and f(x)=b(1-x) for x>=1/2. Make a vector with the numbers xn in it and plot that vector.
2: write matlab code for Histograms of chaos sequences xn+1 = f(xn) where f(x) =r x(1-x). Divide [0,1] into n sub-intervals of length 1/n "bins". Iterate for a random initial condition x0 and count how times xn lies each of these. Plot a histogram of the percent of times each bin is visited.

## Solution Preview

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function hist_logistic(r,x0,N,n_bins)
%Inputs
% r -- the coefficient of f(x)=rx(1-x); r should be in the range of 0 to 4
% x0 -- initial condition (.5 default)
% N -- the number of iterates for which to draw the cobweb (100 default)
% n_bins -- number of bins to use in the histogram. (100 default)
%   Usage:
%   hist_logistic(3.99,.5,100000)...
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