How to generate a golden ratio graph in simulink

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Ragavendra Joshi
Ragavendra Joshi el 15 de Abr. de 2023
Comentada: Ragavendra Joshi el 23 de Abr. de 2023
I want to generate a golden ratio graph using xy graph block. Can someone help me?
  2 comentarios
Sam Chak
Sam Chak el 15 de Abr. de 2023
Can you at least show the golden ratio equation in MATLAB code format for the plotting purposes?
Ragavendra Joshi
Ragavendra Joshi el 16 de Abr. de 2023
I don't have code for the golden ratio, but I do have one for a spiral trajectory. Can you help me to implement this trajectory in Simulink?
% Spiral trajectory parameters
a = 1; % Scale factor
b = 0.2; % Angular frequency
h = 0.1; % Height above the ground
% Time vector
t = 0:0.01:10;
x = a * exp(b*t) .* cos(t);
y = a * exp(b*t) .* sin(t);
theta = atan2(y,x) + h*t;
traj = timeseries([x', y', theta', t'], t');
plot(x,y);
xlabel('X position');
ylabel('Y position');
title('Spiral Trajectory');

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Sam Chak
Sam Chak el 16 de Abr. de 2023
Editada: Sam Chak el 18 de Abr. de 2023
18 Apr 2023 (Update): Here are the basic blocks in Simulink that you can use to create the Golden Ratio Spiral plot. The simulation time is , the same as shown in the MATLAB code. Max Step size is set to 0.001.
16 Apr 2023: If you are looking to show something like this, then modify the code to plot for a longer arclength.
t = linspace(0, 2*pi, 1000);
% define the Golden Ratio constant
phi = (1 + sqrt(5)) / 2;
% define parametric equations
x = cos(t);
y = sin(t);
x_phi = cos(t) .* exp(phi*t/(2*pi));
y_phi = sin(t) .* exp(phi*t/(2*pi));
% plotting
figure;
plot(x, y, 'Color', '#A7B7F7', 'linewidth', 2);
hold on;
plot(x_phi, y_phi, 'Color', '#3952B2', 'linewidth', 2);
legend('Circle', 'Golden Spiral');
title('Parametric equation of the Golden Ratio');
% other settings
grid on
axis equal;
box off;
  13 comentarios
Sam Chak
Sam Chak el 23 de Abr. de 2023
Oh I see. You can '_smoothen_' the plot by running the sim at a smaller step size. Go to the config menu and set the max step size to 0.01 or 1e-3.
Ragavendra Joshi
Ragavendra Joshi el 23 de Abr. de 2023
Thanks a lot!

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