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//
//
// chaos~
// Copyright (C) 2004 Tim Blechmann
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; see the file COPYING. If not, write to
// the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
// Boston, MA 02111-1307, USA.
#include "map_base.hpp"
#include <cmath>
// ikeda laser map: z[n+1] = roh + c2 * z[n] *
// exp (j * (c1 - c3 / (1 + abs(z) * abs(z))))
// z is complex
//
// equal: x[n+1] = roh + c2 * (x[n] * cos(tau) - y[n] * sin (tau))
// y[n+1] = c2 * (x[n] * sin(tau) + y[n] * cos(tau))
// tau = c1 - (c2 / (1 + x*x + y*y))
//
// taken from Willi-Hans Steeb: Chaos and Fractals
class ikeda_laser_map:
public map_base<1>
{
public:
ikeda_laser_map()
{
CHAOS_PAR_INIT(c1,0.4);
CHAOS_PAR_INIT(c2,0.9);
CHAOS_PAR_INIT(c3,9);
CHAOS_PAR_INIT(roh,0.85);
CHAOS_SYS_INIT(x,0.5,0);
CHAOS_SYS_INIT(y,0.5,1);
}
void m_step()
{
data_t x = m_data[0];
data_t y = m_data[1];
data_t tau = CHAOS_PARAMETER(c1) -
CHAOS_PARAMETER(c3) / (1 + x*x + y*y);
data_t cos_tau = cos(tau);
data_t sin_tau = sin(tau);
m_data[0] = CHAOS_PARAMETER(roh) + CHAOS_PARAMETER(c2)
* (x * cos_tau - y * sin_tau);
m_data[1] = CHAOS_PARAMETER(c2) * (x * sin_tau + y * cos_tau);
}
CHAOS_SYSVAR_FUNCS(x, 0);
CHAOS_SYSVAR_FUNCS(y, 1);
CHAOS_SYSPAR_FUNCS(c1);
CHAOS_SYSPAR_FUNCS(c2);
CHAOS_SYSPAR_FUNCS(c3);
CHAOS_SYSPAR_FUNCS(roh);
};
#define IKEDA_LASER_MAP_CALLBACKS \
MAP_CALLBACKS; \
CHAOS_SYS_CALLBACKS(c1); \
CHAOS_SYS_CALLBACKS(c2); \
CHAOS_SYS_CALLBACKS(c3); \
CHAOS_SYS_CALLBACKS(roh); \
CHAOS_SYS_CALLBACKS(x); \
CHAOS_SYS_CALLBACKS(y);
#define IKEDA_LASER_MAP_ATTRIBUTES \
MAP_ATTRIBUTES; \
CHAOS_SYS_ATTRIBUTE(c1); \
CHAOS_SYS_ATTRIBUTE(c2); \
CHAOS_SYS_ATTRIBUTE(c3); \
CHAOS_SYS_ATTRIBUTE(roh); \
CHAOS_SYS_ATTRIBUTE(x); \
CHAOS_SYS_ATTRIBUTE(y);
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