




import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

UpperCamelCase__ :    str 					=							0.25 + 0.0J
UpperCamelCase__ :    Any 					=							-0.4 + 0.6J
UpperCamelCase__ :    List[str] 					=							-0.1 + 0.651J
UpperCamelCase__ :    Any 					=							-2.0
UpperCamelCase__ :    int 					=							56
UpperCamelCase__ :    Dict 					=							2.0
UpperCamelCase__ :    Union[str, Any] 					=							6_66




def       snake_case__	(       lowerCAmelCase   :		complex				,					lowerCAmelCase   :		numpy.ndarray		):
					return numpy.exp(lowerCAmelCase		) + c_parameter




def       snake_case__	(       lowerCAmelCase   :		complex				,					lowerCAmelCase   :		numpy.ndarray		):
					return z_values * z_values + c_parameter




def       snake_case__	(       lowerCAmelCase   :		float				,					lowerCAmelCase   :		int		):
					__snake_case          =	numpy.linspace(-window_size				,					lowerCAmelCase				,					lowerCAmelCase		)
					__snake_case          =	x.reshape((nb_pixels, 1)		)
					__snake_case          =	numpy.linspace(-window_size				,					lowerCAmelCase				,					lowerCAmelCase		)
					__snake_case          =	y.reshape((1, nb_pixels)		)
					return x + 1.0J * y




def       snake_case__	(       lowerCAmelCase   :		Callable[[Any, numpy.ndarray], numpy.ndarray]				,					lowerCAmelCase   :		Any				,					lowerCAmelCase   :		int				,					lowerCAmelCase   :		numpy.ndarray				,					lowerCAmelCase   :		float | None = None				,					):
					__snake_case          =	z_a.astype("""complex64"""		)
					for _ in range(lowerCAmelCase		):
										__snake_case          =	eval_function(lowerCAmelCase				,					lowerCAmelCase		)
										if infinity is not None:
															numpy.nan_to_num(lowerCAmelCase				,					copy=lowerCAmelCase				,					nan=lowerCAmelCase		)
															__snake_case          =	infinity
					return z_n




def       snake_case__	(       lowerCAmelCase   :		str				,					lowerCAmelCase   :		Any				,					lowerCAmelCase   :		float				,					lowerCAmelCase   :		numpy.ndarray				,					):
					__snake_case          =	(abs(lowerCAmelCase		)).transpose()
					__snake_case          =	abs_z_final[::-1, :]
					pyplot.matshow(abs_z_final < escape_radius		)
					pyplot.title(F'''Julia set of ${function_label}$, $c={function_params}$'''		)
					pyplot.show()




def       snake_case__	(       ):
					warnings.filterwarnings(
					    """ignore"""				,					category=lowerCAmelCase				,					message="""overflow encountered in multiply"""		)
					warnings.filterwarnings(
					    """ignore"""				,					category=lowerCAmelCase				,					message="""invalid value encountered in multiply"""				,					)
					warnings.filterwarnings(
					    """ignore"""				,					category=lowerCAmelCase				,					message="""overflow encountered in absolute"""		)
					warnings.filterwarnings(
					    """ignore"""				,					category=lowerCAmelCase				,					message="""overflow encountered in exp"""		)


if __name__ == "__main__":
		UpperCamelCase__ :    Tuple 					=							prepare_grid(window_size, nb_pixels)

		ignore_overflow_warnings()  # See file header for explanations

		UpperCamelCase__ :    Union[str, Any] 					=							24
		UpperCamelCase__ :    List[str] 					=							2 * abs(c_cauliflower) + 1
		UpperCamelCase__ :    Union[str, Any] 					=							iterate_function(
		    eval_quadratic_polynomial,
		    c_cauliflower,
		    nb_iterations,
		    z_a,
		    infinity=1.1 * escape_radius,
		)
		show_results("z^2+c", c_cauliflower, escape_radius, z_final)

		UpperCamelCase__ :    str 					=							64
		UpperCamelCase__ :    List[Any] 					=							2 * abs(c_polynomial_a) + 1
		UpperCamelCase__ :    Union[str, Any] 					=							iterate_function(
		    eval_quadratic_polynomial,
		    c_polynomial_a,
		    nb_iterations,
		    z_a,
		    infinity=1.1 * escape_radius,
		)
		show_results("z^2+c", c_polynomial_a, escape_radius, z_final)

		UpperCamelCase__ :    Dict 					=							1_61
		UpperCamelCase__ :    Union[str, Any] 					=							2 * abs(c_polynomial_a) + 1
		UpperCamelCase__ :    Optional[Any] 					=							iterate_function(
		    eval_quadratic_polynomial,
		    c_polynomial_a,
		    nb_iterations,
		    z_a,
		    infinity=1.1 * escape_radius,
		)
		show_results("z^2+c", c_polynomial_a, escape_radius, z_final)

		UpperCamelCase__ :    str 					=							12
		UpperCamelCase__ :    str 					=							10000.0
		UpperCamelCase__ :    Tuple 					=							iterate_function(
		    eval_exponential,
		    c_exponential,
		    nb_iterations,
		    z_a + 2,
		    infinity=1.0e10,
		)
		show_results("e^z+c", c_exponential, escape_radius, z_final)








"""simple docstring"""

from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize
class     A__      (      lowercase_     ):
	A_							:				Tuple						     =      1
	A_							:				Union[str, Any]						     =      2
	A_							:				Union[str, Any]						     =      3




	def __repr__(   self  :	Dict	)					-> Union[str, Any]:
						return f'''{self.__class__.__name__}.{self.name}'''




def       snake_case__	(       lowerCAmelCase   :		tuple[int, int]				,					lowerCAmelCase   :		int				,					lowerCAmelCase   :		int		):
					__snake_case      ,      __snake_case          =	point
					return degrees(atana(y - miny				,					x - minx		)		)




def       snake_case__	(       lowerCAmelCase   :		tuple[int, int]				,					lowerCAmelCase   :		tuple[int, int]				,					lowerCAmelCase   :		tuple[int, int]		):
					__snake_case      ,      __snake_case          =	starting
					__snake_case      ,      __snake_case          =	via
					__snake_case      ,      __snake_case          =	target
					__snake_case          =	degrees(atana(ya - ya				,					xa - xa		)		)
					via_angle %= 360
					__snake_case          =	degrees(atana(ya - ya				,					xa - xa		)		)
					target_angle %= 360
					# t-
					#  \ \
					#   \ v
					#    \|
					#     s
					# via_angle is always lower than target_angle, if direction is left.
					# If they are same, it means they are on a same line of convex hull.
					if target_angle > via_angle:
										return Direction.left
					elif target_angle == via_angle:
										return Direction.straight
					else:
										return Direction.right




def       snake_case__	(       lowerCAmelCase   :		list[tuple[int, int]]		):

					if len(lowerCAmelCase		) <= 2:
										# There is no convex hull
										raise ValueError("""graham_scan: argument must contain more than 3 points."""		)
					if len(lowerCAmelCase		) == 3:
										return points
					# find the lowest and the most left point
					__snake_case          =	0
					__snake_case      ,      __snake_case          =	maxsize, maxsize
					for i, point in enumerate(lowerCAmelCase		):
										__snake_case          =	point[0]
										__snake_case          =	point[1]
										if y < miny:
															__snake_case          =	y
															__snake_case          =	x
															__snake_case          =	i
										if y == miny and x < minx:
															__snake_case          =	x
															__snake_case          =	i

    # remove the lowest and the most left point from points for preparing for sort
					points.pop(lowerCAmelCase		)

					__snake_case          =	sorted(lowerCAmelCase				,					key=lambda lowerCAmelCase		: angle_comparer(lowerCAmelCase				,					lowerCAmelCase				,					lowerCAmelCase		)		)
					# This insert actually costs complexity,
					# and you should instead add (minx, miny) into stack later.
					# I'm using insert just for easy understanding.
					sorted_points.insert(0				,					(minx, miny)		)

					__snake_case          =	deque()
					stack.append(sorted_points[0]		)
					stack.append(sorted_points[1]		)
					stack.append(sorted_points[2]		)
					# In any ways, the first 3 points line are towards left.
					# Because we sort them the angle from minx, miny.
					__snake_case          =	Direction.left

					for i in range(3				,					len(lowerCAmelCase		)		):
										while True:
															__snake_case          =	stack[-2]
															__snake_case          =	stack[-1]
															__snake_case          =	sorted_points[i]
															__snake_case          =	check_direction(lowerCAmelCase				,					lowerCAmelCase				,					lowerCAmelCase		)

															if next_direction == Direction.left:
																				__snake_case          =	Direction.left
																				break
															if next_direction == Direction.straight:
																				if current_direction == Direction.left:
																									# We keep current_direction as left.
																									# Because if the straight line keeps as straight,
																									# we want to know if this straight line is towards left.
																									break
																				elif current_direction == Direction.right:
																									# If the straight line is towards right,
																									# every previous points on those straigh line is not convex hull.
																									stack.pop()
															if next_direction == Direction.right:
																				stack.pop()
										stack.append(sorted_points[i]		)
					return list(lowerCAmelCase		)


