



"""simple docstring"""






import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
		# Create universe of discourse in Python using linspace ()
		_lowercase				:				Dict   		=		np.linspace(start=0, stop=7_5, num=7_5, endpoint=True, retstep=False)

		# Create two fuzzy sets by defining any membership function
		# (trapmf(), gbellmf(), gaussmf(), etc).
		_lowercase				:				str   		=		[0, 2_5, 5_0]
		_lowercase				:				int   		=		[2_5, 5_0, 7_5]
		_lowercase				:				int   		=		fuzz.membership.trimf(X, abca)
		_lowercase				:				str   		=		fuzz.membership.trimf(X, abca)

		# Compute the different operations using inbuilt functions.
		_lowercase				:				Tuple   		=		np.ones(7_5)
		_lowercase				:				Optional[int]   		=		np.zeros((7_5,))
		# 1. Union = max(µA(x), µB(x))
		_lowercase				:				str   		=		fuzz.fuzzy_or(X, young, X, middle_aged)[1]
		# 2. Intersection = min(µA(x), µB(x))
		_lowercase				:				Tuple   		=		fuzz.fuzzy_and(X, young, X, middle_aged)[1]
		# 3. Complement (A) = (1- min(µA(x))
		_lowercase				:				int   		=		fuzz.fuzzy_not(young)
		# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
		_lowercase				:				List[Any]   		=		fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
		# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
		_lowercase				:				Union[str, Any]   		=		young + middle_aged - (young * middle_aged)
		# 6. Algebraic Product = (µA(x) * µB(x))
		_lowercase				:				Optional[int]   		=		young * middle_aged
		# 7. Bounded Sum = min[1,(µA(x), µB(x))]
		_lowercase				:				Any   		=		fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
		# 8. Bounded difference = min[0,(µA(x), µB(x))]
		_lowercase				:				List[str]   		=		fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

		# max-min composition
		# max-product composition

		# Plot each set A, set B and each operation result using plot() and subplot().
		from matplotlib import pyplot as plt

		plt.figure()

		plt.subplot(4, 3, 1)
		plt.plot(X, young)
		plt.title("Young")
		plt.grid(True)

		plt.subplot(4, 3, 2)
		plt.plot(X, middle_aged)
		plt.title("Middle aged")
		plt.grid(True)

		plt.subplot(4, 3, 3)
		plt.plot(X, union)
		plt.title("union")
		plt.grid(True)

		plt.subplot(4, 3, 4)
		plt.plot(X, intersection)
		plt.title("intersection")
		plt.grid(True)

		plt.subplot(4, 3, 5)
		plt.plot(X, complement_a)
		plt.title("complement_a")
		plt.grid(True)

		plt.subplot(4, 3, 6)
		plt.plot(X, difference)
		plt.title("difference a/b")
		plt.grid(True)

		plt.subplot(4, 3, 7)
		plt.plot(X, alg_sum)
		plt.title("alg_sum")
		plt.grid(True)

		plt.subplot(4, 3, 8)
		plt.plot(X, alg_product)
		plt.title("alg_product")
		plt.grid(True)

		plt.subplot(4, 3, 9)
		plt.plot(X, bdd_sum)
		plt.title("bdd_sum")
		plt.grid(True)

		plt.subplot(4, 3, 1_0)
		plt.plot(X, bdd_difference)
		plt.title("bdd_difference")
		plt.grid(True)

		plt.subplots_adjust(hspace=0.5)
		plt.show()









"""simple docstring"""






import colorsys

from PIL import Image  # type: ignore






def   snake_case__     (	__lowerCamelCase       :					float							,	__lowerCamelCase       :					float							,	__lowerCamelCase       :					int			):
			"""simple docstring"""
			lowerCamelCase__	:	Optional[Any]				=x
			lowerCamelCase__	:	Any				=y
			for step in range(__lowerCamelCase			):  # noqa: B007
						lowerCamelCase__	:	List[Any]				=a * a - b * b + x
						lowerCamelCase__	:	Optional[int]				=2 * a * b + y
						lowerCamelCase__	:	Union[str, Any]				=a_new

						# divergence happens for all complex number with an absolute value
						# greater than 4
						if a * a + b * b > 4:
									break
			return step / (max_step - 1)






def   snake_case__     (	__lowerCamelCase       :					float			):
			"""simple docstring"""
			if distance == 1:
						return (0, 0, 0)
			else:
						return (255, 255, 255)






def   snake_case__     (	__lowerCamelCase       :					float			):
			"""simple docstring"""
			if distance == 1:
						return (0, 0, 0)
			else:
						return tuple(round(i * 255			) for i in colorsys.hsv_to_rgb(__lowerCamelCase							,	1							,	1			)			)






def   snake_case__     (	__lowerCamelCase       :					int = 800							,	__lowerCamelCase       :					int = 600							,	__lowerCamelCase       :					float = -0.6							,	__lowerCamelCase       :					float = 0							,	__lowerCamelCase       :					float = 3.2							,	__lowerCamelCase       :					int = 50							,	__lowerCamelCase       :					bool = True							,	):
			"""simple docstring"""
			lowerCamelCase__	:	Optional[Any]				=Image.new('''RGB'''							,	(image_width, image_height)			)
			lowerCamelCase__	:	Optional[int]				=img.load()

			# loop through the image-coordinates
			for image_x in range(__lowerCamelCase			):
						for image_y in range(__lowerCamelCase			):
									# determine the figure-coordinates based on the image-coordinates
									lowerCamelCase__	:	Optional[Any]				=figure_width / image_width * image_height
									lowerCamelCase__	:	Dict				=figure_center_x + (image_x / image_width - 0.5) * figure_width
									lowerCamelCase__	:	Optional[int]				=figure_center_y + (image_y / image_height - 0.5) * figure_height

									lowerCamelCase__	:	Any				=get_distance(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase			)

									# color the corresponding pixel based on the selected coloring-function
									if use_distance_color_coding:
												lowerCamelCase__	:	int				=get_color_coded_rgb(__lowerCamelCase			)
									else:
												lowerCamelCase__	:	Optional[int]				=get_black_and_white_rgb(__lowerCamelCase			)

			return img


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# colored version, full figure
		_lowercase				:				Optional[Any]   		=		get_image()

		# uncomment for colored version, different section, zoomed in
		# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
		# figure_width = 0.8)

		# uncomment for black and white version, full figure
		# img = get_image(use_distance_color_coding = False)

		# uncomment to save the image
		# img.save("mandelbrot.png")

		img.show()




