The Letter "N" as Attractor

on 16 Oct 2022

% Inspired by the work of Paul Bourke

% see http://paulbourke.net/fractals/N/

N=1e8;

x=single(zeros(N,1)); % required for speed up

y=x;

% N-Attractor - discrete system

for k=1:N-1

c0=1.7; %1.6831349342542232;

c1=-3; %-2.9984035545418575;

c2=2.12; %2.1207267208634164;

c3=-c2; %-2.121518002564899;

u=x(k);

v=y(k);

X=u*(u*u+1)/2;

Y=v*(v*v+1)/2;

x(k+1)=c0*sin(v-Y)+c1*tanh(u-X);

y(k+1)=c2*sin(u-X)+c3/cosh(v-Y);

end

I=ones(800);

D=size(I,1);

for k=1:N

W=ceil(D*(x(k)+5)/10);

U=ceil(D-D*(y(k)+5)/8);

I(U,W)=I(U,W)-1e-3;

end

imshow(I);

axis equal;