uses java.math.BigDecimal
uses java.lang.System

static function sqrt(x : BigDecimal) : BigDecimal {
  var guess : BigDecimal = x / 2
  var step : BigDecimal = guess / 2
  var minstep : BigDecimal = (1 as BigDecimal).divide((10 as BigDecimal).pow(x.scale()+1))
  while(step > minstep) {
    if(guess*guess < x) {
      guess += step
    } else {
      guess -= step
    }
    step = step.divide(2)
  }
  return guess
}

static class Complex {
  var a : BigDecimal
  var b : BigDecimal

  construct(that : Complex) {
    a = that.a
    b = that.b
  }

  construct(x : BigDecimal, y : BigDecimal) {
    a = x
    b = y
  }

  function add(that : Complex) {
    this.a += that.a
    this.b += that.b
  }

  function mul(that : Complex) {
    this.a = this.a * that.a - this.b * that.b
    this.b = this.a * that.b + this.b * that.a
  }

  function r()  : BigDecimal {
    return sqrt(this.a.pow(2) + this.b.pow(2))
  }

  function rsquared() : BigDecimal { // like Euclidean distance but with out the square root because BigDecimal doesn't have a sqrt
    return this.a.pow(2) + this.b.pow(2)
  }

  override function toString() : String {
    return "(${this.a}, ${this.b})"
  }
}

function mandelbrot(c : Complex, max : int) : int {
  var n = 0
  var z = new Complex(0,0)
  //while(n < max and z.r() < 2) { // slooooow
  while(n < max and z.rsquared() < 4) {
    z.mul(z)
    z.add(c)
    n += 1

    //print(z.a.scale())
  }
  return n
}

var center = new Complex(0,0)
var scale : BigDecimal = 10
var grid : int = 35
var escape : int = 9

function mapGridPoint(x : int, y : int) : Complex {
  return new Complex(
    BigDecimal.ONE / scale * (x - grid / 2) + center.a,
    BigDecimal.ONE / scale * (y - grid / 2) + center.b
  )
}

function write(s : String) {
  System.out.print(s)
}

for(i in 0..grid) {
  //write("| ")
  for(j in 0..grid) {
    var c = mapGridPoint(j, i)
    var iterations = mandelbrot(c, escape)
    write(" ")
    if(iterations == escape) write("*")
    else write(".")
    System.out.flush()
  }
  write("\n")
}