You are trying to animate the Lemniscate of Bernoulli, here is an example in rectangular co-ordinate system
clear
clc;
h=animatedline;
xlim([-1.5 1.5]);
ylim([-1.5 1.5]);
h.LineWidth=1.5;
% parametric representation of Lemniscate of Bernoulli
t = linspace(-4,4,10000);
x = cos(t)./(1+(sin(t).^2));
y = (sin(t).*cos(t))./(1+(sin(t).^2));
for k = 1:10000
addpoints(h,x(k),y(k))
drawnow
end
the above is simple cartesian representation however while doing the polar representation you have to take care of angles as negative quantities cannot be present inside the square root sign as they would lead to complex number so your angles should be constrained, the representation in polar co-ordinates you require is given below
clear;
figure;
h = animatedline(polaraxes);
rlim([0 1]);
h.LineWidth = 1.5;
h.Color=[1 0 0] ;
theta = -pi/4:0.001:pi/4; % cosine of 2*theta will be positive for this range
n= length(theta);
% first half animation
r = -sqrt(cos(2*theta));
for k = 1:length(theta)
addpoints(h,theta(k),r(k))
drawnow
end
% second half animation
r = sqrt(cos(2*theta)); % the negative sign covers second half
theta = pi/4:-0.001:-pi/4;
for k = 1:length(theta)
addpoints(h,theta(k),r(k))
drawnow
end
I hope the above two code snippets achieve your end goal, please accept the answer if the query is answered. Thank you
