It is a generative artwork of De Jong attractors on polar coordinates.

 

Yet another way of drawing with De Jong attractors.

It's a creative coding artwork made with the 'Processing'.

I had an idea that draws De Jong attractors on polar coordinates. There is various way to draw on polar coordinates, and I choose this way.

    // De Jong Attractors
    float currX = sin(TWO_PI * djA * prevY) - cos(TWO_PI * djB * prevX);
    float currY = sin(TWO_PI * djC * prevX) - cos(TWO_PI * djD * prevY);

    // polar coordinates
    float dX = width  * 0.15 * currX;
    float dY = height * 0.15 * currX;
    float dR = rBase * currY;
    float px = dX * cos(dR) - dY * sin(dR);
    float py = dY * cos(dR) + dX * sin(dR);

There is a convergence problem in drawing attractors. I tried to avoid this by changing the attractor parameter in recurrence.

    // for avoid convergence (as much as possible)
    if (pCnt == floor(pMax * 0.6)){
      djA = random(-1.0, 1.0);
      djB = 1.0;
      djC = random(-1.0, 1.0);
      djD = 1.0;
    }

 

Calculation variations.

Ball

    float px = width  * sin(_x * _y) * cos(_r * _x);
    float py = height * cos(_x * _y) * sin(_r * _y);

 

Square

    float px = width  * sin(_x) * cos(PI * _x);
    float py = height * cos(_y) * sin(PI * _y);

 

Cloth

    float px = width  * sin(_y) * cos(PI * _x);
    float py = height * cos(_x) * sin(PI * _y);

 

The 'Processing' example code.

This code does not display any images on the screen but generates image files in frames directory.

Please feel free to use this example code of the 'Processing' under the terms of the GPL. To see other works based on my code is my pleasure. And my honor.

/**
 * Just Another Nervous Wreck.
 * 
 * A creative coding that draws De Jong attractors on polar coordinates.
 * 
 * Processing 3.5.3
 * @author @deconbatch
 * @version 0.1
 * created 0.1 2020.01.26
 */

void setup() {

  size(980, 980);
  colorMode(HSB, 360, 100, 100, 100);
  rectMode(CENTER);
  smooth();
  noLoop();

}

void draw() {

  int   frmMax  = 3;
  float hueBase = random(360);

  translate(width / 2, height / 2);
  for (int frmCnt = 0; frmCnt < frmMax; frmCnt++) {

    blendMode(DIFFERENCE);
    background(0.0, 0.0, 90.0, 100.0);
    hueBase += 90.0;

    pushMatrix();
    rotate(random(PI));
    drawWreck(hueBase);
    popMatrix();  
    
    blendMode(BLEND);
    casing(hueBase);
    
    saveFrame("frames/" + String.format("%04d", frmCnt + 1) + ".png");
  }
  exit();
}

/**
 * drawWreck : draws De Jong attractors on polar coordinates
 * @param  _hueBase : drawing color.
 */
void drawWreck(float _hueBase) {

  float hueBase = _hueBase;

  // De Jong Attractor parameters
  float djA   = 1.0;
  float djB   = random(-1.0, 1.0);
  float djC   = 1.0;
  float djD   = random(-1.0, 1.0);
  float prevX = random(-2.0, 2.0);
  float prevY = random(-2.0, 2.0);

  float rBase = random(0.2, 0.5) * HALF_PI;
  float sBase = 0.25;
  int   pMax  = 12000000;

  noStroke();
  for (int pCnt = 0; pCnt < pMax; pCnt++) {

    // for avoid convergence (as much as possible)
    if (pCnt == floor(pMax * 0.6)){
      djA = random(-1.0, 1.0);
      djB = 1.0;
      djC = random(-1.0, 1.0);
      djD = 1.0;
      hueBase += 30.0;
    }

    // De Jong Attractors
    float currX = sin(TWO_PI * djA * prevY) - cos(TWO_PI * djB * prevX);
    float currY = sin(TWO_PI * djC * prevX) - cos(TWO_PI * djD * prevY);

    // polar coordinates
    float dX = width  * 0.15 * currX;
    float dY = height * 0.15 * currX;
    float dR = rBase * currY;
    float px = dX * cos(dR) - dY * sin(dR);
    float py = dY * cos(dR) + dX * sin(dR);
    float ps = sBase * (1.0 + dist(px, py, 0.0, 0.0) * 2.0 / width);

    fill(hueBase % 360.0, 40.0, 15.0, 100.0);
    ellipse(px, py, ps, ps);

    prevX = currX;
    prevY = currY;

  }
}


/**
 * casing : draw fancy casing
 * @param  _hueBase : casing color.
 */
private void casing(float _hueBase) {
  
  fill(0.0, 0.0, 0.0, 0.0);
  strokeWeight(40.0);
  stroke(_hueBase, 60.0, 20.0, 100.0);
  rect(0.0, 0.0, width, height);
  strokeWeight(30.0);
  stroke(0.0, 0.0, 95.0, 100.0);
  rect(0.0, 0.0, width, height);
    
}

/*
Copyright (C) 2019- deconbatch

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 3 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.  If not, see <http://www.gnu.org/licenses/>
*/

 

Yet another example images of this generative art.