Chaos game on a square with 2 points away restriction

on 6 Oct 2021

N=10^5;

v=zeros(N,2);

a=4;

%vertices and centre of a square

c=[[0,1];[1,1];[1,0];[0,0]];

plot(c(:,1),c(:,2),'.',markersize=20);

p=[0,0];

lc=1;

for i=1:N

idx = randi(a);

%Restriction: The next point cannot be two vertices away.

%Can only be the same point or immediate neighbours

while idx==(mod(lc+1,a)+1)

idx = randi(a);

end

lc=idx;

s=c(idx,:);

p=(p+s)/2;

v(i,:)=p;

end

plot(v(:,1),v(:,2),'.',markersize=1)

xlim([0,1])

ylim([0,1])

axis off

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