Attractors
Rössler attractor
The image shown in the right column is rendered in Sunflow. Any renderer that has sphere primitive can be used to generate such images. This formula gives the x,y and z coordinates, these values can be exported as the center of the sphere primitive in that renderer .
numPoints = 100000;
x = zeros(1,numPoints);
y = zeros(1,numPoints);
z = zeros(1,numPoints);
x(1) = 0;%0.10001;
y(1) = 0;%-0.10001;
z(1) = 0;%0.10001;
dt = 0.02;
a = 0.2;
b = 0.2;
c = 8.0;
for n = 2:numPoints
x(n) = x(n-1)+ dt*(-y(n-1)-z(n-1));
y(n) = y(n-1)+ dt*(x(n-1)+a*y(n-1));
z(n) = z(n-1)+ dt*(b+z(n-1)*(x(n-1)-c));
end
% draw connecting line
line(x,y,z,'LineWidth',0.5,'Color',[0.2 0.3 0.5]);
view(3)
axis on equal
box on
% draw only the points
figure
line(x,y,z,'Marker','.'...
,'Markersize',1,...
'Linestyle','none',...
'Color',[0.2 0.3 0.5]);
view(3)
axis on equal
box on
Henon attractor
% equation
% x(n+1)=y(n)+1-1.4*x(n)^2
% y(n+1)=0.3*x(n);
numPoints = 15000; % number of points in attrcator
x = zeros(1,numPoints);
y = zeros(1,numPoints);
x(1) = 0; %starting x point
y(1) = 0; %starting y point
a = 1.4;
b = 0.3;
for n = 2:numPoints
x(n) = y(n-1)+1-a*x(n-1)^2;
y(n) = b*x(n-1);
end
plot(x,y,'.','MarkerSize',1);
scatter(x,y,1,x);
colormap hsv
axis on