Generating Zero-Mean Gaussian Numbers Using Uniform Random Numbers

Here's an example program in C that generates zero-mean Gaussian numbers using the suggested method and plots a histogram of the results using the 'gnuplot' library:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "gnuplot.h"

#define NUM_SAMPLES 10000

double generate_gaussian()
{
    double sum = 0.0;
    for (int i = 0; i < 12; i++) {
        sum += (double)rand() / RAND_MAX;
    }
    return sum - 6.0;
}

int main()
{
    // Seed the random number generator
    srand(time(NULL));

    // Generate Gaussian numbers
    double samples[NUM_SAMPLES];
    for (int i = 0; i < NUM_SAMPLES; i++) {
        samples[i] = generate_gaussian();
    }

    // Plot histogram
    gnuplot_ctrl *handle;
    handle = gnuplot_init();
    gnuplot_setstyle(handle, "boxes");
    gnuplot_cmd(handle, "set title 'Histogram of Gaussian Numbers'");
    gnuplot_cmd(handle, "set xlabel 'Value'");
    gnuplot_cmd(handle, "set ylabel 'Frequency'");
    gnuplot_cmd(handle, "set xrange [-10:10]");
    gnuplot_cmd(handle, "set yrange [0:500]");
    gnuplot_cmd(handle, "binwidth=0.1");
    gnuplot_cmd(handle, "bin(x,width)=width*floor(x/width)");
    gnuplot_cmd(handle, "plot '-' using (bin($1,binwidth)):(1.0) smooth freq with boxes");
    for (int i = 0; i < NUM_SAMPLES; i++) {
        gnuplot_cmd(handle, "%lf", samples[i]);
    }
    gnuplot_cmd(handle, "e");

    // Wait for user input before closing the plot window
    printf("Press enter to exit...");
    getchar();

    // Cleanup
    gnuplot_close(handle);

    return 0;
}

This program uses the 'gnuplot' library to plot the histogram of the generated Gaussian numbers. You'll need to have the 'gnuplot' library installed and linked with your program. The program generates 10,000 Gaussian numbers using the suggested method and stores them in the 'samples' array. It then plots the histogram using 'gnuplot_cmd' function calls.

To compile the program, save it in a file called 'gaussian.c' and use the following command:

gcc -o gaussian gaussian.c -lm -lgnuplot_c

After running the program, a plot window will open showing the histogram of the generated Gaussian numbers. The region of the histogram that looks most Gaussian will have a symmetrical bell-shaped curve around zero. The region that looks least Gaussian will have more irregularities or deviations from the bell-shaped curve.