File:Fubini Nightmare foliation Katok example.svg

#include <iostream>
#include <math.h>
#include <vector>
#include <time.h>
#include <stdlib.h>
#include <assert.h>

using namespace std;
double F(double p, vector<int> a, int N)
{
	assert(p>0 && p<1);
	int i;
	double x=0;
	double q=1-p;
	for(i=0;i<N;i++)
	{
		if(a[i]==1)
		{
			x+=q;
			q*=p;
		}
		else
		{
			q*=(1-p);
		}
	}
	return x;
}

main()
{
	srand(time(NULL));
	vector<int> a;
	double prec=2E-3;
	int N=int(1/(prec*prec));
	int exp=500;
	int i,j;
	double p;
	bool first=true;
	cout << "import graph;\nimport math;\nimport fontsize;\nunitsize(7inch);\ndefaultpen(0.45mm);\n" << endl;
	for(i=0;i<exp;i++)
	{
		a.clear();
		for(j=0;j<N;j++)
		{
			a.push_back(rand()%2);
		}
		first=true;
		for(p=2*prec;p<1-2*prec;p+=prec)
		{
			if(first)
			{
				cout << "draw(";
				first=false;
			}
			else
			{
				cout << "--";
			}
			cout << "(" << p << "," << F(p,a,N) << ")" ;
		}
		cout << ");" << endl;
	}
	cout << "xaxis(\"$p$\",BottomTop,fontsize(48));\nyaxis(\"$x$\",LeftRight,fontsize(48));" << endl;
}