



"""simple docstring"""







from __future__ import annotations

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

# initial triangle of Koch snowflake
A    =			numpy.array([0, 0])
A    =			numpy.array([0.5, 0.866_0254])
A    =			numpy.array([1, 0])
A    =			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							list[numpy.ndarray]:
       A         =					initial_vectors
       for _ in range(lowerCamelCase__			):
              A         =					iteration_step(lowerCamelCase__			)
       return vectors

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list[numpy.ndarray]:
       A         =					[]
       for i, start_vector in enumerate(vectors[:-1]			):
              A         =					vectors[i + 1]
              new_vectors.append(lowerCamelCase__			)
              A         =					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   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							numpy.ndarray:
       A         =					numpy.radians(lowerCamelCase__			)
       A      ,  A         =					numpy.cos(lowerCamelCase__			), numpy.sin(lowerCamelCase__			)
       A         =					numpy.array(((c, -s), (s, c))			)
       return numpy.dot(lowerCamelCase__				,      lowerCamelCase__			)

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							None:
       A         =					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         =					zip(*lowerCamelCase__			)
       plt.plot(lowerCamelCase__				,      lowerCamelCase__			)
       plt.show()


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       A    =			iterate(INITIAL_VECTORS, 5)
       plot(processed_vectors)








"""simple docstring"""







import re

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list:
							return [char.split() for char in re.split(R'[^ a-z A-Z 0-9 \s]'				,      str_			)]

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							A         =					split_input(str_			)
							return "".join(
							    [''.join([char.capitalize() for char in sub_str]			) for sub_str in string_split]			)

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							try:
														A         =					split_input(lowerCamelCase__			)
														if upper:
																					A         =					''.join(
																					    [
																					        separator.join([char.upper() for char in sub_str]			)
																					        for sub_str in string_split
																					    ]			)
														else:
																					A         =					''.join(
																					    [
																					        separator.join([char.lower() for char in sub_str]			)
																					        for sub_str in string_split
																					    ]			)
														return res_str
							except IndexError:
														return "not valid string"

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							return to_simple_case(lowerCamelCase__			)

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							try:
														A         =					to_simple_case(lowerCamelCase__			)
														return res_str[0].lower() + res_str[1:]
							except IndexError:
														return "not valid string"

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							return to_complex_case(lowerCamelCase__				,      lowerCamelCase__				,      '_'			)

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							return to_complex_case(lowerCamelCase__				,      lowerCamelCase__				,      '-'			)


if __name__ == "__main__":
							__import__('doctest').testmod()



