Lorenz System (Attractor) is a system of Ordinary Differential Equations, that a group of special parameters are applied to.

odeint is a boost c++ library that can solve Lorenz System.

The shape of the graphical path looks like a bufferfly, so it is also well-known as "bufferfly effect".

ODE :

dx/dt := Sigma * (y - x)
dy/dt := Ro * x - y - x * z
dz/dt := x * y - Beta * z

Read first: c++ boost odeint ODE

c++ example

#include <boost/numeric/odeint.hpp>
#include <functional>
#include <iostream>
#include <vector>

namespace odeint = boost::numeric::odeint;

namespace nsb
{
	using std::placeholders::_1;
	using std::placeholders::_2;
	using std::placeholders::_3;

	using dfloat = float;
	using state_type = std::vector<nsb::dfloat>;
}

namespace nsb
{
	class equation
	{
	private:
		const nsb::dfloat S = 10;	// sigma
		const nsb::dfloat R = 28;	// ro
		const nsb::dfloat B = 8.0/3.0;	// beta
	public:
		void system(const nsb::state_type & x, nsb::state_type & dxdt, const nsb::dfloat t) const
		{
			auto x0 = x[0]; auto x1 = x[1]; auto x2 = x[2];
			auto & dx0dt = dxdt[0]; auto & dx1dt = dxdt[1]; auto & dx2dt = dxdt[2];
			dx0dt = S * (x1 - x0);
			dx1dt = R * x0 - x1 - x0 * x2;
			dx2dt = x0 * x1 - B * x2;
		}
		void observer(const nsb::state_type & x, const nsb::dfloat t) const
		{
			std::cout << t << "\t\t" << x[0] << "\t" << x[1] << "\t" << std::endl;
		}
	public:
		void run() const
		{
			state_type init{0.3, 0.1, 0.5};
			odeint::integrate_const(
				odeint::runge_kutta4<nsb::state_type>{},
				std::bind(
					&nsb::equation::system,
					this,
					_1,
					_2,
					_3
				),
				init,
				nsb::dfloat{0},
				nsb::dfloat{25},
				nsb::dfloat{0.1},
				std::bind(
					&nsb::equation::observer,
					this,
					_1,
					_2
				)
			);
		}
	};
}

int main()
{
	nsb::equation eqt;
	eqt.run();
}

Date

Sat Jun 7 06:03:31 AM UTC 2025

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