How to generate a golden ratio graph in simulink

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Ragavendra Joshi
Ragavendra Joshi 2023-4-15
评论： Ragavendra Joshi 2023-4-23
I want to generate a golden ratio graph using xy graph block. Can someone help me?
  2 个评论
Sam Chak
Sam Chak 2023-4-15
Can you at least show the golden ratio equation in MATLAB code format for the plotting purposes?
Ragavendra Joshi
Ragavendra Joshi 2023-4-16
Ran in:
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 2023-4-16
编辑：Sam Chak 2023-4-18
Ran in:
Hi @Ragavendra Joshi
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;
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Sam Chak
Sam Chak 2023-4-23
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.

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