tst

%% wykres

clear variables;

T=2e3;
T0=T-2e1;
mi=3.8;
f=@(x,mi) mi.*x.*(1-x);

x(1)=0.4;
for t=1:T-1
    x(t+1)=f(x(t),mi);
end

X=0:1e-3:1;Y=X;
clf; hold on; grid on;
plot(X,Y);
plot(X,f(X,mi),'linewidth',1);
plot(X,f(f(f(f(X,mi),mi),mi),mi),'linewidth',1);

for t=1+T0:T-1
   plot([x(t), f(x(t),mi)],[f(x(t),mi),f(x(t),mi)],'Color',0.75*[1,1,1]);
   plot([f(x(t),mi), f(x(t),mi)],[f(x(t),mi),f(x(t+1),mi)],'Color',0.75*[1,1,1]);

end

plot(x(1+T0:T-1),x(2+T0:T),'o')
axis equal;

%% wykres bifurkacyjny

clear variables;
clf;hold on; grid on;
T=2e0;
min=2e3;

mi=linspace(2.8,4,min);
N=10;
x(1)=0.5;
f=@(x,mi) mi.*x.*(1-x);

for miIdx=1:min

    for n=1:T-1, x(n+1)=f(x(n),mi(miIdx)); end
    for t=n:n+N
        x(t+1)=f(x(t),mi(miIdx));
        plot(mi(miIdx),x(t), '.k', 'MarkerSize',2);
    end

end

%% ostatnie

clear variables;

a=-0.04;
p=[0.85, 0.92, 0.99, 1];
A1=[0.85 a; -a -0.85]; b1=[0;16];
A2=[0.2 -0.26; 0.23 0.22]; b2=[0; 1.6];
A3=[-0.15 0.28; 0.26 0.24]; b3=[0; 0.44];
A4=[0 0; 0 0.16];


x=rand(2,1);
clf;hold on;
for t=1:5e3
    r=rand;
    if r<p(1)
        x=A1*x+b1;
    elseif r<p(2)
        x=A2*x+b2;
    elseif r<p(3)
        x=A3*x+b3;
    else
        x=A4*x;
    end
    plot(x(1),x(2),'.g','MarkerSize',3);
end