Mandelbrot set

You are encouraged to solve this task according to the task description, using any language you may know.


Task

Generate and draw the Mandelbrot set.



Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .




class Complex {
  double _r,_i;
 
  Complex(this._r,this._i);
  double get r => _r;
  double get i => _i;
  String toString() => "($r,$i)";
 
  Complex operator +(Complex other) => new Complex(r+other.r,i+other.i);
  Complex operator *(Complex other) =>
      new Complex(r*other.r-i*other.i,r*other.i+other.r*i);
  double abs() => r*r+i*i;
}
 
void main() {
  double start_x=-1.5;
  double start_y=-1.0;
  double step_x=0.03;
  double step_y=0.1;
 
  for(int y=0;y<20;y++) {
    String line="";
    for(int x=0;x<70;x++) {
      Complex c=new Complex(start_x+step_x*x,start_y+step_y*y);
      Complex z=new Complex(0.0, 0.0);
      for(int i=0;i<100;i++) {
        z=z*(z)+c;
        if(z.abs()>2) {
          break;
        }
      }
      line+=z.abs()>2 ? " " : "*";
    }
    print(line);
  }
}