from PySide import QtCore, QtGui
from math import *
import sys


class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)


class Vector:
    def __init__(self, a, b):
        if type(a) == type(b) == Point:
            self.x = b.x - a.x
            self.y = b.y - a.y
        else:
            self.x = a
            self.y = b

    def __add__(self, other):
        return Vector(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Vector(other.x - self.x, other.y - self.y)

    def __rmul__(self, other):
        if type(other) == Vector:
            return self.x * other.y - self.y * other.x
        return Vector(self.x * (other), self.y *(other))

    def __pow__(self, other):
        return self.x * other.x + self.y * other.y

    def rotation(self, sin, cos):
        return Vector(self.x * cos - self.y * sin, self.x * sin + self.y * cos)


class MyWindow(QtGui.QMainWindow):
    def __init__(self, parent = None):
        QtGui.QMainWindow.__init__(self)
        self.resize(700, 600)
        self.setWindowTitle("Fractal")
        self.setMinimumSize(220, 150)

        self.Widget = MyWidget(self)
        self.Widget.setGeometry(0, 0, self.width(), self.height())

    def resizeEvent(self, event):
        w = self.width()
        h = self.height()
        self.Widget.setGeometry(0, 0, self.width(), self.height())


class MyWidget(QtGui.QWidget):
    def __init__(self, parent = None, N = 5):
        QtGui.QWidget.__init__(self, parent)
        self.type_ = 0
        self.N = N
        self.resize(parent.width(), parent.height())

    def paintEvent(self, event):
        X = self.width()
        Y = self.height()
        if self.type_ == 0:
            if Y * 2 * sqrt(3) >= X:
                P1 = Point(0, Y / 2 + X / 4 / sqrt(3))
                P2 = Point(X, Y / 2 + X / 4 / sqrt(3))
                self.Koch(P1, P2, self.N)
            else:
                P1 = Point(X / 2 - Y * sqrt(3), Y)
                P2 = Point(X / 2 + Y * sqrt(3), Y)
                self.Koch(P1, P2, self.N)

    def Koch(self, P0, P4, n):
        if n == 0:
            painter = QtGui.QPainter()
            painter.begin(self)
            painter.drawLine(P0.x, P0.y, P4.x, P4.y)
            painter.end()
            return
        P1 = P0 + Vector(P0, P4)  * (1 / 3)
        P3 = P0 + Vector(P0, P4) * (2 / 3)
        P2 = P1 + Vector(P1, P0).rotation(sqrt(3) / 2, -0.5)
        self.Koch(P0, P1, n - 1)
        self.Koch(P1, P2, n - 1)
        self.Koch(P2, P3, n - 1)
        self.Koch(P3, P4, n - 1)


app = QtGui.QApplication(sys.argv)
Window = MyWindow()
Window.show()
app.exec_()