





"""simple docstring"""




import sys
import turtle






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       tuple[float, float]       ,			_lowercase		:       tuple[float, float]   )					->tuple[float, float]:






	'''simple docstring'''






	return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       tuple[float, float]       ,			_lowercase		:       tuple[float, float]       ,			_lowercase		:       tuple[float, float]       ,			_lowercase		:       int       ,			)					->None:






	'''simple docstring'''






	my_pen.up()
	my_pen.goto(vertexa[0]       ,			vertexa[1]   )
	my_pen.down()
	my_pen.goto(vertexa[0]       ,			vertexa[1]   )
	my_pen.goto(vertexa[0]       ,			vertexa[1]   )
	my_pen.goto(vertexa[0]       ,			vertexa[1]   )

	if depth == 0:
		return

	triangle(_lowercase       ,			get_mid(_lowercase       ,			_lowercase   )       ,			get_mid(_lowercase       ,			_lowercase   )       ,			depth - 1   )
	triangle(_lowercase       ,			get_mid(_lowercase       ,			_lowercase   )       ,			get_mid(_lowercase       ,			_lowercase   )       ,			depth - 1   )
	triangle(_lowercase       ,			get_mid(_lowercase       ,			_lowercase   )       ,			get_mid(_lowercase       ,			_lowercase   )       ,			depth - 1   )


if __name__ == "__main__":
		if len(sys.argv) != 2:
				raise ValueError(
				    '''Correct format for using this script: '''
				    '''python fractals.py <int:depth_for_fractal>'''
				)
		a		:					List[str]	      =     turtle.Turtle()
		my_pen.ht()
		my_pen.speed(5)
		my_pen.pencolor('''red''')

		a		:					Optional[Any]	      =     [(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
		triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))









"""simple docstring"""




from numpy import exp, pi, sqrt






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Tuple       ,			_lowercase		:       float = 0.0       ,			_lowercase		:       float = 1.0   )					->int:






	'''simple docstring'''






	return 1 / sqrt(2 * pi * sigma**2   ) * exp(-((x - mu) ** 2) / (2 * sigma**2)   )


if __name__ == "__main__":
		import doctest

		doctest.testmod()


