This section shows some more details of one of the simplest type of agent defined by position and direction and explores variation of this type with various behaviors.

The basic structure of this type of agent is described in the following code. The class definition includes two instance field of IVec, pos and dir and each represents the position of the agent in the 3D space and the direction of the agent to generate the next child agent.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    new MyAgent(pos2,dir2);
    del();
  }
}

The code above doesn't show anything when you run the code because it doesn't include any methods to create geometries.

In the setup() method, an instance of MyAgent is created taking two ninput vectors. The first input vector is passed to the position vector and the second is to the direction vector in the constructor of MyAgent class. In the update() method, the direction vector dir is added to the position vector pos. However, this code uses cp() method like pos.cp(dir), which copies the instance and add the input value, instead of add() method like pos.add(dir) because not to change the content of pos in case it's used to create geometries or checked by other agents later. Because of this reason, the moved position with the direction vector is assigned to the new instance of IVec pos2. In the same way, the direction vector dir is copied to dir2 in case dir is used later (if you pass dir directly to the child agent and the child agent change dir inside the child, dir in the parent is also changed). Then these new position pos2 and new direction dir2 are used to create a new child agent at this line.
new MyAgent(pos2,dir.cp());
At the end of update() the agent is deleted with del() method because this agent is designed just to generate one child and stop.

The following code generates points at the position of each agent. It also limit the duration of execution for 50 times.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(50);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    new IPoint(pos);
    new MyAgent(pos2,dir2);
    del();
  }
}

Now you can see the behavior of the agent as straight movement in x-axis direction because the direction vector is defined as (1,0,0) in the setup() method at the constructor of MyAgent and the direction vector dir is just copied to dir2 and its content is never changed.

The following code generates lines instead of points between the position of the agent and another position of the next agent.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(50);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    new ICurve(pos,pos2);
    new MyAgent(pos2,dir2);
    del();
  }
}

To control the whole behavior of this type of agents, it's best to control the transformation of the direction vector. The following code shows some simple transformations. The first code below adds some value in y-axis to the direction vector. As a result of accumulation of y value in the direction vector, the whole trace of the agents forms a parabolic curve.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(50);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.add(0,0.1,0);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The next code is adding a negative value in x-axis as well as adding a positive value in y-axis.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(50);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.add(-0.1,0.1,0);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The next code has the same transformation of addition as the previous code but the initial direction vector is different. The initial direction is (2, -4, 0), instead of (1, 0, 0). An initial condition is also important factor to define the behavior of agents as well as an update transformation rule.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(50);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(2,-4,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.add(-0.1,0.1,0);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

Here are more variations of transformation of the direction vector. The first one below shows an example of simple rotation by rotating each direction vector slightly around the zaxis (i.e. on the xy-plane). As an accumulation of small rotation, it forms a circle or an arc depending on the duration of the execution.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(200);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.rot(IG.zaxis, PI/100);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

Another example below combines rotation and multiplication (scaling) of a vector. It rotates and slightly shrinks the vector by 0.999. As a result, it forms swirling curve.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(1000);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.rot(IG.zaxis, PI/100);
    dir2.mul(0.999);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The example below changes the angle to rotate and the multiplier (scaling factor) to multiply the direction vector. Because the rotation vector is large and not clear number, it forms totally different geometry from the swirling curve in the previous example.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(100);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(100,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.rot(IG.zaxis, PI*0.89);
    dir2.mul(1.01);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The following examples use if-condition to switch transformations controlling the behavior of agents depending on their status.

The first one below changes the rotation angle and scaling factor depending on the x component of the direction.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(500);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(dir2.x() > 0){
      dir2.rot(IG.zaxis, PI/80);
      dir2.mul(0.999);
    }
    else{
      dir2.rot(IG.zaxis, PI/40);
      dir2.mul(1.01);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The example below has 4 if-conditions to switch the cases either when the x-direction is positive or negative or the y-direction is positive or negative, and then it sets the new direction in each case.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(100);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(dir2.x() > 0 ){
      dir2.set( 0, dir2.x(), 0);
    }
    else if(dir2.y() > 0){
      dir2.set( -dir2.y()-1, 0, 0);
    }
    else if(dir2.x() < 0){
      dir2.set( 0, dir2.x(), 0);
    }
    else if(dir2.y() < 0){
      dir2.set( -dir2.y()+1, 0, 0);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The example below has if-condition to check x component of the position, instead of the direction. Because when x position is positive, the direction is pushed to negative in x, and otherwise positive in x, as result it oscillates around x=0.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(500);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(2,1,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(pos2.x() > 0){
      dir2.add(-0.1, 0, 0);
    }
    else{
      dir2.add(0.1, 0, 0);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The following codes use IG.time() method to switch the behavior by the time frame of the system.

The example below switches three transformation rules by the time of 0 - 99, 100 - 199, 200 - with the following if-condition statements.
      if( IG.time() < 100 ){ ... }
      else if( IG.time() < 200 ){ ... }
      else{ ... }

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(250);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(0,2,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(IG.time() < 100){
      dir2.rot(IG.zaxis, PI/30);
      dir2.mul(0.99);
    }
    else if(IG.time() < 200){
      dir2.rot(IG.zaxis, -PI/15);
      dir2.mul(1.01);
    }
    else{
      dir2.add(0, -0.05, 0);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

This example below uses remainder operation '%' to the time to define periodical behavior. In the following if condition, the first if-condition part is executed every 15 time frame and other time the second part is executed.
      if( IG.time() % 15 == 0){ ... }
      else{ ... }

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(800);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(IG.time()%15==0){
      dir2.flip();
      dir2.mul(1.01);
    }
    else{
      dir2.rot(IG.zaxis, PI/25);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The following code has more if-condition statements to define more combinational behavior. To define periodical behavior with differentiation in time, it uses a remainder operation '%' and range definition with an inequality operator '<' as well as an equality operator '=='.
      if( IG.time()%50 < 10 ){ ... }
      else if( IG.time()%50 == 10 ){ ... }
      else if( IG.time()%50 < 30 ){ ... }
      else if( IG.time()%50 < 40 ){ ... }
      else if( IG.time()%50 == 40 ){ ... }
      else{ ... }

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(800);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(IG.time()%50 < 10){
      dir2.rot(IG.zaxis, PI/20);
    }
    else if(IG.time()%50 == 10){
      dir2.flip();
    }
    else if(IG.time()%50 < 30){
      dir2.rot(IG.zaxis, PI/11);
    }
    else if(IG.time()%50 < 40){
      dir2.rot(IG.zaxis, -PI/21);
    }
    else if(IG.time()%50 == 40){
      dir2.flip();
    }
    else{
      dir2.rot(IG.zaxis, PI/15);
      dir2.mul(1.01);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

When you use random number to set the transformation of agents, You can get random behavior.

The example below shows an example of random walk agent. It rotates the direction randomly using random number method
    IRand.get(-PI*0.4,PI*0.5)
Note that the minimum range and the maximum range of the random number is not symmetrical around zero and the average number is some positive number. This causes the average behavior to rotate to the positive direction.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(1000);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(0,2,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.rot(IG.zaxis, IRand.get(-PI*0.4, PI*0.5)); //-72deg to +90deg
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

This example below is similar to the code in the previous section "Conditional Transformation 2" but this code switches the behavior by random percentage instead of the time interval inside the if-condition. The randomness method IRand.pct(2.5) returns true in 2.5% probability or false in 97.5%. When you combine this with if-condition, you can switch agent's behavior randomly.
      if( IRand.pct(2.5) ){ ... } //2.5% probability
      else{ ... } //97.5% probability

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(2000);
  MyAgent agent = new MyAgent(IG.v(0,0,0), IG.v(1,0,0));
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(IRand.pct(2.5)){ //2.5% probability
      dir2.flip();
      dir2.mul(1.1);
    }
    else{ //97.5% probability
      dir2.mul(0.996);
      dir2.rot(IG.zaxis, PI/25);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The example codes below add for-loops at setup() method to create multiple instances of the agents with different initial positions and different directions.

This first code is adding multiple instantiation to this previous example with different initial positions on the x-axis and different initial directions towards negative y-directions.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(80);
  for(int i=0; i < 40; i++){
    new MyAgent(IG.v(i*5,0,0), IG.v(1-0.05*i,-0.1*i,0));
  }
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    dir2.add(0,0.1,0);
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}

The following second code is adding multiple instantiation to another previous example with conditional transformation with radial initial positions and phase-shifted radial directions.

import processing.opengl.*;
import igeo.*;

void setup(){
  size(480, 360, IG.GL);
  IG.duration(250);
  int num = 40;
  float inc = 2*PI/num;
  for(int i=0; i < num; i++){
    new MyAgent(IG.v(40*cos(i*inc), 40*sin(i*inc), 0), 
                IG.v(5*cos((i+6)*inc), sin((i+6)*inc), 0));
  }
}

class MyAgent extends IAgent{
  IVec pos, dir;

  MyAgent(IVec p, IVec d){
    pos = p;
    dir = d;
  }

  void update(){
    IVec pos2 = pos.cp(dir);
    IVec dir2 = dir.cp();
    if(pos2.x() > 0){
      dir2.add(-0.1, 0, 0);
    }
    else{
      dir2.add(0.1, 0, 0);
    }
    new ICurve(pos,pos2).clr(0);
    new MyAgent(pos2,dir2);
    del();
  }
}