/*
 *	logistic map
 *	
 *	calculate x_{n+k} vs x_n where k is an integer = 1, 2, ...
 *		this calculation is useful for studying the k-th iterate
 *		of the map
 *
 *	usage: logistic_map2 mu k
 *
 *	mu = control parameters (required)
 *	k = required
 *
 *	by N Giordano -- July 2006
 */

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

double atof();
double logistic();

double mu;
int n_max;

main(argc,argv)
int argc;
char* argv[];
{
	int seed;
	int i,k;
	double dx;
	double f,x;

	if(argc <=1) {
		fprintf(stderr,"usage map mu k\n");
		exit(0);
	}
	mu = atof(argv[1]);
	if(argc >= 3) {
		k = atoi(argv[2]);
	}
	else {
		k = 1;
	}
	dx = 0.01;

	for(x = 0; x <= 1; x += dx) {
		f = logistic(x);
		if(k > 1) f = logistic(f);
		if(k > 2) f = logistic(f);
		printf("%g\t%g\n",x,f);	
	}
}

double logistic(v)
double v;
{
	double val;

	val = mu * v * (1.0 - v);

	return(val);
}