Happy valentine's day 2025 with Nelson

[Nelson-numerical-software]

% Happy Valentine's Day 2025

% Time vector
t = linspace(0, 2*pi, 1000);

% Heart parametric equations
x_heart = 16 .* (sin(t)).^3;
y_heart = 13.*cos(t) - 5.*cos(2.*t) - 2.*cos(3.*t) - cos(4.*t);

% Create figure
f = figure('Color', 'w');

% Colors for hearts
colors = {'red', 'magenta', 'green', 'blue'};
scales = [1, 0.7, 0.5, 0.3];
offsets = [0, 20, -20, 10];

% Draw multiple hearts with different sizes and positions
for i = 1:length(scales)
    x_scaled = scales(i) .* x_heart + offsets(i);
    y_scaled = scales(i) .* y_heart + offsets(i)/2;
    
    fill(x_scaled, y_scaled, colors{i}, 'EdgeColor', 'k', 'LineWidth', 2);
    hold('on');
end

% Add text
text(0, -15, 'Happy Valentine''s Day 🥰', ...
    'FontSize', 14, ...
    'FontWeight', 'bold', ...
    'HorizontalAlignment', 'center', ...
    'Color', 'k');

% Adjust axis properties
axis('equal');
axis('off');

[Nelson-numerical-software]

% Parameters
num_points = 100000; % Number of random points

% Generate random points in the bounding box [-1.5, 1.5] x [-1.5, 1.5]
x = -1.5 + 3 * rand(num_points, 1); % X-coordinates
y = -1.5 + 3 * rand(num_points, 1); % Y-coordinates

% Heart function: (x^2 + y^2 - 1)^3 - x^2*y^3 <= 0
inside_heart = (x.^2 + y.^2 - 1).^3 - x.^2 .* y.^3 <= 0;

% Plot the points
figure;
hold on;
scatter(x(inside_heart), y(inside_heart), 1, 'red', 'filled'); % Points inside the heart
scatter(x(~inside_heart), y(~inside_heart), 1, 'cyan'); % Points outside the heart
axis equal;
xlim([-1.5, 1.5]);
ylim([-1.5, 1.5]);
title('Monte Carlo Heart');
xlabel('x');
ylabel('y');
hold off;