Visualize the irrationality of pi

Mudassir shakeel
/
Visualize the irrationality of pi
on 1 Dec 2023
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drawframe(1);
Write your drawframe function below
function drawframe(f)
function visualization_pi(varargin)
    % Visualize the irrationality of pi
 
    % Default
    FPS = 60;    % Frames per second
    points = 5;  % Number of points to advance
    radius0 = 1; % Radius for the inner arm
    radius1 = 1; % Radius for the outer arm
    
    % Miscellaneous
    color_draw = [0, 0, 0];
    color_arm = [1, 0.5961, 0.0902];
    
    % Get inputs
    for i = 1:2:nargin
        
        switch lower(varargin{i})
            case 'fps'
                FPS = varargin{i + 1};
            case 'points'
                points = varargin{i + 1};
            case 'radius0'
                radius0 = varargin{i + 1};
            case 'radius1'
                radius1 = varargin{i + 1};
        end
    end
    % Define the complex function
    z0 = @(theta) radius0 * exp(1i * theta);
    z1 = @(theta) radius0 * exp(1i * theta) + radius1 * exp(1i * pi * theta);
    
    % Initialize plot
    fig = figure('WindowKeyPressFcn', @keyPressFcn);
    % Plot settings
    hold on;
    axis equal;
    axis off;
    xlim([-1, 1] * (radius0 + radius1));
    ylim([-1, 1] * (radius0 + radius1));
    % Initialization
    timer_val = tic;
    running = true; 
    iteration = 1;
    range = [0, 0];
    line0 = plot(range, range, '-', 'Color', color_arm, 'LineWidth', 1.5);
    line1 = plot(range, range, '-o', 'Color', color_arm, 'LineWidth', 1.5);
    
    while running
        
        % Get values
        real_part = real(z1(range));
        imaginary_part = imag(z1(range));
    
        real_part0 = real(z0(range(end)));
        imaginary_part0 = imag(z0(range(end)));
    
        % Plot
        plot(real_part, imaginary_part, '-', 'Color', color_draw);
        % Update the position of the arms
        set(line0, 'XData', [0, real_part0], 'YData', [0, imaginary_part0]);
        set(line1, 'XData', [real_part0, real_part(end)], 'YData', [imaginary_part0, imaginary_part(end)]);
        % Update title
        titletext = sprintf('Frame %d, Time %.2f [s]', round(range(end) * 180 / pi), toc(timer_val));
        title(titletext, 'Interpreter', 'latex', 'FontSize', 16)
        % Pause to control frame rate
        
    FPS = 30; % Frames per second
dt = 1 / FPS; % Time between frames
while true
    % Your code for each frame here
    
    % Record the start time
    start_time = tic;
    
    % Wait until the desired time has passed
    while toc(start_time) < dt
        % Do nothing and continue waiting
    end
end
        % Update the iteration counter
        iteration = iteration + points;
        
        % Update the range of values to plot
        range = (iteration : (iteration + points)) / 180 * pi;
        % Check if the loop should stop
        if fig.UserData
            running = false;
        end
    end
end
% SUB-PASS FUNCTIONS
function keyPressFcn(obj, input)
    % Callback function for key presses
    % Check if the key pressed is the escape key
    if strcmpi(input.Key, 'escape')
        obj.UserData = true;
    end
end
end
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Visualize the irrationality of pi
Mudassir shakeel