Calculate 2 opposing fibonacci spirals from every point of a circle circumfrence

phi = 0.5*(1+sqrt(5)); % golden ratio

r = phi.^(2*theta/pi); % fibonacci spiral

polarplot(-theta,r,theta,r,theta,-r,-theta,-r) % 2 opposing fibonacci spirals

How can I calculate the trajectories of opposing fibonacci spirals starting from every point of a circle's circumfrence

Answer 1

[Pseudoscientist]

clear all

theta = 0:pi/36:2*pi;

phi = 0.5*(1+sqrt(5));

r = phi.^(2*theta/pi);

r_1=phi.^(2*(-theta)/pi);

testi = exp(1i*theta);

x = r.*cos(theta);

y = r.*sin(theta);

angle=0:pi/36:2*pi;

for i=1:numel(angle)

rot_1{i} = [cos(angle(i)) -sin(angle(i));sin(angle(i)) cos(angle(i))] * [x-1;y+1];

rot_2{i} = [cos(angle(i)) -sin(angle(i));sin(angle(i)) cos(angle(i))] * [1-x;y+1];

end

figure(2)

hold on

for i = 1:numel(rot_1)

plot(rot_1{1,i}(1,:),rot_1{1,i}(2,:),rot_2{1,i}(1,:),rot_2{1,i}(2,:))

end

Answer 2

[Pseudoscientist]

Like this

Answer 3

[Pseudoscientist]

theta = 0:pi/30:2*pi;

phi = 0.5*(1+sqrt(5));

r = phi.^(2*theta/pi);

x = r.*cos(theta);

y = r.*sin(theta);

figure(1);hold on

plot(x-1,1+y,x-1,-1-y,-x+1,1+y,-x+1,-1-y)

plot(cos(theta),sin(theta))