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107 lines
3.4 KiB
Python
107 lines
3.4 KiB
Python
"""
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Langton's ant
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@ https://en.wikipedia.org/wiki/Langton%27s_ant
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@ https://upload.wikimedia.org/wikipedia/commons/0/09/LangtonsAntAnimated.gif
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"""
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from functools import partial
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from matplotlib import pyplot as plt
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from matplotlib.animation import FuncAnimation
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WIDTH = 80
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HEIGHT = 80
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class LangtonsAnt:
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"""
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Represents the main LangonsAnt algorithm.
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>>> la = LangtonsAnt(2, 2)
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>>> la.board
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[[True, True], [True, True]]
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>>> la.ant_position
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(1, 1)
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"""
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def __init__(self, width: int, height: int) -> None:
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# Each square is either True or False where True is white and False is black
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self.board = [[True] * width for _ in range(height)]
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self.ant_position: tuple[int, int] = (width // 2, height // 2)
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# Initially pointing left (similar to the wikipedia image)
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# (0 = 0° | 1 = 90° | 2 = 180 ° | 3 = 270°)
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self.ant_direction: int = 3
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def move_ant(self, axes: plt.Axes | None, display: bool, _frame: int) -> None:
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"""
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Performs three tasks:
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1. The ant turns either clockwise or anti-clockwise according to the colour
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of the square that it is currently on. If the square is white, the ant
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turns clockwise, and if the square is black the ant turns anti-clockwise
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2. The ant moves one square in the direction that it is currently facing
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3. The square the ant was previously on is inverted (White -> Black and
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Black -> White)
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If display is True, the board will also be displayed on the axes
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>>> la = LangtonsAnt(2, 2)
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>>> la.move_ant(None, True, 0)
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>>> la.board
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[[True, True], [True, False]]
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>>> la.move_ant(None, True, 0)
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>>> la.board
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[[True, False], [True, False]]
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"""
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directions = {
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0: (-1, 0), # 0°
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1: (0, 1), # 90°
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2: (1, 0), # 180°
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3: (0, -1), # 270°
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}
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x, y = self.ant_position
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# Turn clockwise or anti-clockwise according to colour of square
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if self.board[x][y] is True:
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# The square is white so turn 90° clockwise
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self.ant_direction = (self.ant_direction + 1) % 4
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else:
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# The square is black so turn 90° anti-clockwise
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self.ant_direction = (self.ant_direction - 1) % 4
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# Move ant
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move_x, move_y = directions[self.ant_direction]
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self.ant_position = (x + move_x, y + move_y)
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# Flip colour of square
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self.board[x][y] = not self.board[x][y]
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if display and axes:
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# Display the board on the axes
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axes.get_xaxis().set_ticks([])
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axes.get_yaxis().set_ticks([])
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axes.imshow(self.board, cmap="gray", interpolation="nearest")
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def display(self, frames: int = 100_000) -> None:
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"""
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Displays the board without delay in a matplotlib plot
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to visually understand and track the ant.
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>>> _ = LangtonsAnt(WIDTH, HEIGHT)
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"""
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fig, ax = plt.subplots()
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# Assign animation to a variable to prevent it from getting garbage collected
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self.animation = FuncAnimation(
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fig, partial(self.move_ant, ax, True), frames=frames, interval=1
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)
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plt.show()
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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LangtonsAnt(WIDTH, HEIGHT).display()
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