processingでローレンツカオス、ヘノンアトラクタ、ロジスティック写像

HenonMap.pde

void setup(){
  size(700,700);
  background(255,255,255);
  drawHenonMap();
}

void draw(){

}

void drawHenonMap(){ 
  float x = 0.1, y = 0.0;
  float a = 1.4, b = 0.3;
  for(int n = 0; n < 100; n++){
    float x_ = 1-a*x*x+y;
    float y_ = b*x;
    x = x_;
    y = y_;
  }
  for(int n = 0; n < 100000; n++){
    float x_ = 1-a*x*x+y;
    float y_ = b*x;
    x = x_;
    y = y_;
    stroke(0,100,255);
    rect(map(x, -1.5,1.5, 0, width), map(y, 0.5,-0.5, 0, height), 1,1);
  }
}

LogisticMap.pde

void setup(){
  size(700,350);
  //background(0);
  logisticMap(2.5, 0.0, 4.0, 1.0);
  noStroke();
}



void draw(){
  
  
}


void logisticMap(float x, float y, float x2, float y2){
  float scaleX = (x2-x)/width;
  float scaleY = (y2-y)/height;
  
  for(int i = 0; i < width; i++){
    float a  = x + i*scaleX;
    float b_ = 0.1;
    float b;
    for(int n = 0; n < 300; n++){
      b  = a*b_*(1-b_);
      b_ = b;
    }
    for(int n = 0; n < 300; n++){
      b  = a*b_*(1-b_);
      point(i, (b-y)/scaleY);
      b_ = b;
    }
  }
  
}

LorenzSystem.pde

RungeKutta rgk;
int fps = 60;
float theta = 90.0f;
float phi = 0.0f;
float distance = 1000.0f;

void setup(){
  size(700,700, P3D);
  background(0);
  frameRate(fps);
  rgk = new RungeKutta(10d, 28d, 8d/3d, 1d,0.5d, 0.5d, 1d/ fps);
  //ortho();
}

void draw(){
  
    camera(distance*sin(theta)*sin(phi), distance*cos(theta), 1000*sin(theta)*cos(phi), // 視点X, 視点Y, 視点Z
     0, 0, 0.0, // 中心点X, 中心点Y, 中心点Z
      0.0, 1.0, 0.0); // 天地X, 天地Y, 天地Z
      
   //degree += 0.05;
   //if(degree >= 360.0) degree = 0.0;
      
   ambientLight(20, 20, 20);    //環境光を当てる
  lightSpecular(255, 255, 255);    //光の鏡面反射色（ハイライト）を設定
  directionalLight(100, 100, 100, 0, 1, -1);    //指向性ライトを設定
      
  drawLorenzKaos();
  updateLorenzKaos();
  delay(10);
}


public void drawLorenzKaos(){
  pushMatrix();
  specular(255, 0,0);
  noStroke();
  translate((float)(rgk.getX()*10), (float)(rgk.getY()*10), (float)(rgk.getZ()*10));
  println("x =" + rgk.getX() +  " y=" + rgk.getY() + " z=" + rgk.getZ());
  box(5,5,5);
  popMatrix();
}

public void updateLorenzKaos(){
  rgk.nextstep();
}

RungeKutta.java

public class RungeKutta {
  
  public double p,r,b,x,y,z,dt;
  
  public RungeKutta(double p, double r, double b,  double initx, double inity, double initz, double dt){
    this.p = p;
    this.r = r;
    this.b = b;
    this.x = initx;
    this.y = inity;
    this.z = initz;
    this.dt = dt;
  }
  
  public void nextstep(){
    double j1[] = new double[4]; //x
    double j2[] = new double[4]; //y
    double j3[] = new double[4]; //z
    
    j1[0] = dt * funcX(x,y,z);
    j2[0] = dt * funcY(x,y,z);
    j3[0] = dt * funcZ(x,y,z);
    
    j1[1] = dt * funcX(x + j1[0]*0.5,y + j2[0] * 0.5 ,z + j2[0] * 0.5);
    j2[1] = dt * funcY(x + j1[0]*0.5,y + j2[0] * 0.5 ,z + j2[0] * 0.5);
    j3[1] = dt * funcZ(x + j1[0]*0.5,y + j2[0] * 0.5 ,z + j2[0] * 0.5);
    
    j1[2] = dt * funcX(x + j1[1]*0.5,y + j2[1] * 0.5 ,z + j2[1] * 0.5);
    j2[2] = dt * funcY(x + j1[1]*0.5,y + j2[1] * 0.5 ,z + j2[1] * 0.5);
    j3[2] = dt * funcZ(x + j1[1]*0.5,y + j2[1] * 0.5 ,z + j2[1] * 0.5);
    
    j1[3] = dt * funcX(x  + j1[2], y + j2[2] ,z + j3[2]);
    j2[0] = dt * funcY(x  + j1[2], y + j2[2] ,z + j3[2]);
    j3[0] = dt * funcZ(x  + j1[2], y + j2[2] ,z + j3[2]);
    
    x += (j1[0] + 2* j1[1] + 2*j1[2] + j1[3])/6.0;
    y += (j2[0] + 2* j2[1] + 2*j2[2] + j2[3])/6.0;
    z += (j3[0] + 2* j3[1] + 2*j3[2] + j3[3])/6.0;
  }
  
  private double funcX(double x, double y, double z){
    return -p*x+p*y;
  }
  
  private double funcY(double x, double y, double z){
    return -x*z+r*x-y;
  }
  
   private double funcZ(double x, double y, double z){
    return x*y-b*z;
  }
  
  public double getX(){
    return x;
  }
  
  public double getY(){
    return y;
  }
  
  public double getZ(){
    return z;
  }
  
}