






'''simple docstring'''



from __future__ import annotations

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

# initial triangle of Koch snowflake
__UpperCamelCase      :       Dict      			=      numpy.array([0, 0])
__UpperCamelCase      :       Any      			=      numpy.array([0.5, 0.866_0254])
__UpperCamelCase      :       Any      			=      numpy.array([1, 0])
__UpperCamelCase      :       str      			=      [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	list[numpy.ndarray],					SCREAMING_SNAKE_CASE__:	int    )  ->			list[numpy.ndarray]:

   """simple docstring"""
   __a				     =    initial_vectors
   for _ in range(SCREAMING_SNAKE_CASE__    ):
      __a				     =    iteration_step(SCREAMING_SNAKE_CASE__    )
   return vectors



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	list[numpy.ndarray]    )  ->			list[numpy.ndarray]:

   """simple docstring"""
   __a				     =    []
   for i, start_vector in enumerate(vectors[:-1]    ):
      __a				     =    vectors[i + 1]
      new_vectors.append(SCREAMING_SNAKE_CASE__    )
      __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    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	numpy.ndarray,					SCREAMING_SNAKE_CASE__:	float    )  ->			numpy.ndarray:

   """simple docstring"""
   __a				     =    numpy.radians(SCREAMING_SNAKE_CASE__    )
   __a     ,			__a				     =    numpy.cos(SCREAMING_SNAKE_CASE__    ), numpy.sin(SCREAMING_SNAKE_CASE__    )
   __a				     =    numpy.array(((c, -s), (s, c))    )
   return numpy.dot(SCREAMING_SNAKE_CASE__,					SCREAMING_SNAKE_CASE__    )



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	list[numpy.ndarray]    )  ->			None:

   """simple docstring"""
   __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(*SCREAMING_SNAKE_CASE__    )
   plt.plot(SCREAMING_SNAKE_CASE__,					SCREAMING_SNAKE_CASE__    )
   plt.show()


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 __UpperCamelCase      :       Dict      			=      iterate(INITIAL_VECTORS, 5)
 plot(processed_vectors)







'''simple docstring'''



import warnings

from .generation import TFGenerationMixin
class 							__SCREAMING_SNAKE_CASE       (							_lowerCAmelCase     ):
      # warning at import time
      warnings.warn(
          "Importing `TFGenerationMixin` from `src/transformers/generation_tf_utils.py` is deprecated and will "
          "be removed in Transformers v5. Import as `from transformers import TFGenerationMixin` instead."      ,      _lowerCAmelCase      ,      )