/*
 *	logistic map
 *	
 *	record x_n+1 vs x_n
 *		useful for studying return maps and period doubling behavior
 *
 *	by N Giordano -- July 2006
 *
 *	usage: logistic_map3 mu [x_0] [n_max]
 *
	mu = control parameter (should be between 0 and 4)
	x_0 = initial value of x (optional)
	n_max = number of iterations (optional)
 *
 *	write results to standard output
 */

#include <math.h>
#include <stdio.h>

double atof();

double mu;
double x_new,x_old;
int n_max;

main(argc,argv)
int argc;
char* argv[];
{
	int seed;
	int i;

/* initialize parameters	*/
	if(argc <=1) {
		fprintf(stderr,"usage map mu [x_0] [n_max]\n");
		exit(0);
	}
	mu = atof(argv[1]);
	x_new = 0;
	if(argc >= 3) {
		x_old = atof(argv[2]);
	}
	else {
		x_old = 0.314159;
	}
	if(argc >= 4) {
		n_max = atoi(argv[3]);
	}
	else {
		n_max = 100;
	}

/* do the actual calculation here	*/
	printf("%g\t%g\n",x_old,x_new);	
	for(i = 1; i < n_max; i++) {
		x_new = mu * x_old * (1.0 - x_old);
		printf("%g\t%g\n",x_old,x_new);	
		x_old = x_new;
		printf("%g\t%g\n",x_old,x_new);	
	}
}