
"""simple docstring"""


def  lowercase						(	lowerCAmelCase__						):
			return " ".join(input_str.split()[::-1]						)


if __name__ == "__main__":
						import doctest

						doctest.testmod()










"""simple docstring"""




from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
a		:					int	      =     numpy.array([0, 0])
a		:					Optional[Any]	      =     numpy.array([0.5, 0.866_0254])
a		:					Tuple	      =     numpy.array([1, 0])
a		:					List[str]	      =     [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list[numpy.ndarray]       ,			_lowercase		:       int   )					->list[numpy.ndarray]:






	'''simple docstring'''






	a :						List[str]      =							initial_vectors
	for _ in range(_lowercase   ):
		a :						Optional[Any]      =							iteration_step(_lowercase   )
	return vectors






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list[numpy.ndarray]   )					->list[numpy.ndarray]:






	'''simple docstring'''






	a :						Union[str, Any]      =							[]
	for i, start_vector in enumerate(vectors[:-1]   ):
		a :						str      =							vectors[i + 1]
		new_vectors.append(_lowercase   )
		a :						Optional[int]      =							end_vector - start_vector
		new_vectors.append(start_vector + difference_vector / 3   )
		new_vectors.append(
		    start_vector + difference_vector / 3 + rotate(difference_vector / 3       ,			60   )   )
		new_vectors.append(start_vector + difference_vector * 2 / 3   )
	new_vectors.append(vectors[-1]   )
	return new_vectors






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       numpy.ndarray       ,			_lowercase		:       float   )					->numpy.ndarray:






	'''simple docstring'''






	a :						int      =							numpy.radians(_lowercase   )
	a,			a :						Optional[int]      =							numpy.cos(_lowercase   ), numpy.sin(_lowercase   )
	a :						Dict      =							numpy.array(((c, -s), (s, c))   )
	return numpy.dot(_lowercase       ,			_lowercase   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list[numpy.ndarray]   )					->None:






	'''simple docstring'''






	a :						Dict      =							plt.gca()
	axes.set_aspect("equal"   )

	# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
	# y-coordinates as inputs, which are constructed from the vector-list using
	# zip()
	a,			a :						Any      =							zip(*_lowercase   )
	plt.plot(_lowercase       ,			_lowercase   )
	plt.show()


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		a		:					Optional[int]	      =     iterate(INITIAL_VECTORS, 5)
		plot(processed_vectors)


