barrymartin.cpp

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// -*- Mode:C++; Coding:us-ascii-unix; fill-column:158 -*-
/*******************************************************************************************************************************************************.H.S.**/
/**
 @file      barrymartin.cpp
 @author    Mitch Richling <https://www.mitchr.me>
 @brief     Draw some Barry Martin Attractors.@EOL
 @std       C++20
 @see       https://www.mitchr.me/SS/barrymartin/index.html
 @copyright
  @parblock
  Copyright (c) 1988-2015, Mitchell Jay Richling <https://www.mitchr.me> All rights reserved.
 
  Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
 
  1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
 
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
     and/or other materials provided with the distribution.
 
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
     without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  DAMAGE.
  @endparblock
 @filedetails   
 
  Barry Martin's "Hopalong" orbit fractals are a family of discrete-time dynamical systems:
     - Classic Barry Martin fractal:
       @f[  \begin{align*}
              x_{n+1} & = y_n - \mathrm{sgn}(x_n) \cdot \sqrt{\vert b x_n-c\vert} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
     - Positive Barry Martin fractal:
       @f[  \begin{align*}
              x_{n+1} & = y_n + \mathrm{sgn}(x_n) \cdot \sqrt{\vert b x_n-c\vert} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
     - Additive Barry Martin fractal:
       @f[  \begin{align*}
              x_{n+1} & = y_n + \sqrt{\vert b x_n-c\vert} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
     - Sinusoidal Barry Martin fractal:
       @f[  \begin{align*}
              x_{n+1} & = y_n + \sin{(b x_n-c)} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
  
  All of these maps, and others, may be constructed from the following system as special cases:
    @f[  \begin{align*}
           x_{n+1} & = y_n+d \cdot \mathrm{ssgn}(x_n) \cdot \left(f \cdot \sqrt{\vert b x_n-c\vert} + g \cdot \sin{(b x_n-c)} + h \cdot \vert b x_n-c\vert \right) \\
           y_{n+1} & = a-x_n
         \end{align*} @f]
    Where
    @f[  \mathrm{ssgn}(v) = \cases{ s & $v\lt 0$ \cr
                                    1 & $v\ge 0$ } @f]
    @f[  \mathrm{sgn}(v) = \cases{ -1 & $v\lt 0$ \cr
                                   +1 & $v\ge 0$ } @f]
 
    Note the simplified form of the @f$\mathrm{sgn}(v)@f$ function used -- the standard definition may be used for nearly identical results.
  
    Some special cases:
     - When @f$ d=-1, s=-1, f=1, g=0, h=0 @f$, the map becomes the "Classic Barry Martin fractal"
     - When @f$ d=1, s=-1, f=1, g=0, h=0 @f$, the map becomes the "Positive Barry Martin fractal"
     - When @f$ d=1, s=1, f=1, g=0, h=0 @f$, the map becomes the "Additive Barry Martin fractal"
     - When @f$ d=1, s=1, f=0, g=1, h=0, c=0 @f$, the map becomes the "Sinusoidal Barry Martin fractal"
     - When @f$ d=1, s=1, f=0, g=0, h=1, c=0 @f$, the map becomes the "The Gingerbread Man":
       @f[  \begin{align*}
              x_{n+1} & = y_n + \sin{(b x_n)} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
     - When @f$ d=1, s=1, f=0, g=0, h=1, c\ne0 @f$, the map becomes the "The Shifted Gingerbread Man":
       @f[  \begin{align*}
              x_{n+1} & = y_n + \sin{(b x_n-c)} \\ 
              y_{n+1} & = a-x_n
            \end{align*} @f]
*/
/*******************************************************************************************************************************************************.H.E.**/
/** @cond exj */
 
//--------------------------------------------------------------------------------------------------------------------------------------------------------------
#include "ramCanvas.hpp"
#include "MRMathSTR.hpp"
 
//--------------------------------------------------------------------------------------------------------------------------------------------------------------
std::vector<std::array<double, 14>> params {
  /*        a         b         c       d,      s,   f,   g,   h,     n,   k, x-min, x-max,  y-min, y-max */
  {  -2.00000, -0.33000,  0.01000,   -1.0,   -1.0, 1.0, 0.0, 0.0, 4.0e7, 1.0, -18.0,  17.0,  -18.0,  17.0}, //  0 
  {   0.40000,  1.10000,  0.00000,   -1.0,   -1.0, 1.0, 0.0, 0.0, 2.5e7, 1.0,  -7.0,   7.0,   -7.0,   7.0}, //  1 
  {  -3.14000,  0.20000,  0.30000,   -1.0,   -1.0, 1.0, 0.0, 0.0, 3.0e7, 1.0, -40.0,  40.0,  -40.0,  40.0}, //  2 
  {  -3.14000,  0.19000,  0.32000,    1.0,   -1.0, 1.0, 0.0, 0.0, 1.0e7, 1.0, -38.0,  35.0,  -38.0,  35.0}, //  3 
  {  -2.14000, -0.20000,  0.30000,    1.0,    1.0, 1.0, 0.0, 0.0, 3.0e7, 0.5,  -9.0,   7.0,   -9.0,   7.0}, //  4 
  {   0.40000,  1.00000,  0.00000,   -1.0,   -1.0, 0.0, 1.0, 0.0, 2.0e6, 1.0, -70.0,  70.0,  -70.0,  70.0}, //  5 
  {  -3.14000,  0.20000,  0.30000,   -1.0,   -1.0, 0.0, 1.0, 0.0, 6.0e7, 1.0, -45.0,  45.0,  -45.0,  45.0}, //  6 
  {  -3.14000,  0.20000,  0.30000,    1.0,   -1.0, 0.0, 1.0, 0.0, 1.0e7, 1.0, -35.0,  35.0,  -35.0,  35.0}, //  7 
  {  -2.00000, -0.33000,  0.01000,   -1.0,   -1.0, 1.0, 0.0, 1.0, 4.0e7, 1.0, -25.0,  25.0,  -25.0,  25.0}, //  8 
  {  -3.14000,  0.20000,  0.30000,   -1.0,   -1.0, 1.0, 0.0, 1.0, 4.0e7, 1.0, -60.0,  60.0,  -60.0,  60.0}, //  9 
  {  -3.14000,  0.20000,  0.30000,    1.0,   -1.0, 1.0, 0.0, 1.0, 6.0e7, 1.0, -90.0,  90.0,  -90.0,  90.0}, // 10 
  {  -3.14000,  0.20000,  0.30000,   -1.0,   -1.0, 0.0, 0.0, 1.0, 2.0e7, 1.0, -17.0,  15.0,  -17.0,  15.0}, // 11 
  {  -3.14000,  0.20000,  0.30000,    1.0,   -1.0, 0.0, 0.0, 1.0, 3.0e7, 1.0, -17.0,  14.0,  -17.0,  14.0}, // 12 
  {  -3.14000,  0.20000,  0.30000,    1.0,   -1.0, 0.0, 0.0, 1.0, 1.0e7, 1.0, -17.0,  14.0,  -17.0,  14.0}, // 13 
  {  -1.14000,  0.01000,  0.05000,    1.0,   -1.0, 0.0, 0.0, 1.0, 5.0e6, 1.0,  -3.5,   2.5,   -3.5,   2.5}, // 14 
  {  -1.14000,  0.10000,  0.50000,    1.0,   -1.0, 0.0, 0.0, 1.0, 6.0e7, 1.0, -17.0,  14.0,  -17.0,  14.0}, // 15 
};
 
//--------------------------------------------------------------------------------------------------------------------------------------------------------------
int main(void) {
  std::chrono::time_point<std::chrono::system_clock> startTime = std::chrono::system_clock::now();
  const int BSIZ = 480*8;
  mjr::ramCanvas1c16b::colorType aColor;
  aColor.setChans(1);
 
  for(decltype(params.size()) j=0; j<params.size(); ++j) {
    mjr::ramCanvas1c16b theRamCanvas(BSIZ, BSIZ, params[j][10], params[j][11], params[j][12], params[j][13]);
 
    double a = params[j][0];
    double b = params[j][1];
    double c = params[j][2];
    double d = params[j][3];
    double s = params[j][4];
    double k = params[j][9];
 
    double f = params[j][5];
    double g = params[j][6];
    double h = params[j][7];
 
    /* Draw the Attractor on a 16-bit, greyscale canvas such that the level is the hit count for that pixel.  
       Thus we are using an "image" as a way to store field data instead of color information. */
    double x        = 0.0;
    double y        = 0.0;
    uint64_t maxII  = 0;
    uint64_t inCnt  = 0;
    uint64_t maxItr = static_cast<uint64_t>(params[j][8]);
    uint64_t iPrt   = maxItr / 5;
    for(uint64_t i=1;i<maxItr;i++) {
      double xNew = y+d*(x<0.0?s:1.0)* (f*std::sqrt(std::abs(b*x-c)) + g*std::sin(b*x-c) + h*std::abs(b*x-c));
      double yNew = a-x;
      if ( !theRamCanvas.isCliped(x, y)) {
        inCnt++;
        theRamCanvas.drawPoint(x, y, theRamCanvas.getPxColor(x, y).tfrmAdd(aColor));
        if(theRamCanvas.getPxColor(x, y).getC0() > maxII) {
          maxII = theRamCanvas.getPxColor(x, y).getC0();
          if(maxII > 16384) { // 1/4 of max possible intensity
            std::cout << "ITER(" << j <<  "): " << i << " MAXS: " << maxII << " EXIT: Maximum image intensity reached" << std::endl;
            break;
          }
        }
      }
      if((i % iPrt) == 0)
        std::cout << "ITER(" << j <<  "): " << i << " MAXS: " << maxII << " INC: " << inCnt << std::endl;
      x=xNew;
      y=yNew;
    }
    std::cout << "ITER(" << j <<  "): " << "DONE" << " MAXS: " << maxII << " INC: " << inCnt << std::endl;
 
    // Log image transform
    theRamCanvas.applyHomoPixTfrm(&mjr::ramCanvas1c16b::colorType::tfrmLn1);
    maxII = static_cast<uint64_t>(std::log(static_cast<double>(maxII)));
 
    /* Create a new image based on csCCfractal0RYBCW -- this one is 24-bit RGB color. */
    mjr::ramCanvas3c8b anotherRamCanvas(BSIZ, BSIZ);
    typedef mjr::ramCanvas3c8b::colorType::csCCfractal0RYBCW cs_t;
    for(int yi=0;yi<theRamCanvas.getNumPixY();yi++)
      for(int xi=0;xi<theRamCanvas.getNumPixX();xi++) 
        anotherRamCanvas.drawPoint(xi, yi, cs_t::c(k * theRamCanvas.getPxColor(xi, yi).getC0() / static_cast<mjr::ramCanvas3c8b::csFltType>(maxII)));
 
    anotherRamCanvas.writeTIFFfile("barrymartin_" + mjr::math::str::fmt_int(j, 2, '0') + ".tiff");
  }
  std::chrono::duration<double> runTime = std::chrono::system_clock::now() - startTime;
  std::cout << "Total Runtime " << runTime.count() << " sec" << std::endl;
  return 0;
}
/** @endcond */