#include <iostream>
#include <cstdlib>
#include <cmath>     //for sin, cos, atan2
using namespace std;

struct color {
	unsigned char red;	//can hold integers in range 0 to 255 inclusive
	unsigned char green;
	unsigned char blue;
};

int main()
{
	const size_t width = 750;
	const size_t height = width;
	color a[width][height];

	const int xmax = width / 2;	//Place origin at center.
	const int ymax = height / 2;

	const int xmin = xmax - width;
	const int ymin = ymax - height;

	const color white = {255, 255, 255};
	const color blue  = {  0,   0, 255};
	const color black = {  0,   0,   0};

	for (int x = xmin; x < xmax; ++x) {
		for (int y = ymin; y < ymax; ++y) {
			if (x == 0 || y == 0) {
				a[x - xmin][y - ymin] = blue;	//axes
			} else {
				a[x - xmin][y - ymin] = white;	//background
			}
		}
	}

	const int n = 3 * width;	//number of points to plot
	const double pi = 4.0 * atan2(1.0, 1.0);

	for (int i = 0; i < n; ++i) {
		//The fraction i/n goes from 0 to almost 1,
		//so theta goes from 0 to almost 2 * pi radians.

		const double theta = 2 * pi * i / n;
		const double r = sin(3 * theta);	//flower with 3 petals

		const int x = static_cast<int>(r * cos(theta) * xmax);
		const int y = static_cast<int>(r * sin(theta) * ymax);

		if (xmin <= x && x < xmax && ymin <= y && y < ymax) {
			a[x - xmin][y - ymin] = black;
		}
	}

	cout << "P3\n"	//magic number of Netpbm .ppm file
		<< width << " " << height << "\n"
		<< 255 << "\n";	//maximum color value; 0 is minimum

	for (int y = ymax - 1; y >= ymin; --y) {
		for (int x = xmin; x < xmax; ++x) {
			const color c = a[x - xmin][y - ymin];

			//Cast makes the unsigned chars print in decimal.
			cout
				<< static_cast<int>(c.red) << "\t"
				<< static_cast<int>(c.green) << "\t"
				<< static_cast<int>(c.blue) << "\n";
		}
	}

	return EXIT_SUCCESS;
}