#### Langtons Ant

I
```"""
Langton's ant

@ https://en.wikipedia.org/wiki/Langton%27s_ant
"""

from functools import partial

from matplotlib import pyplot as plt
from matplotlib.animation import FuncAnimation

WIDTH = 80
HEIGHT = 80

class LangtonsAnt:
"""
Represents the main LangonsAnt algorithm.

>>> la = LangtonsAnt(2, 2)
>>> la.board
[[True, True], [True, True]]
>>> la.ant_position
(1, 1)
"""

def __init__(self, width: int, height: int) -> None:
# Each square is either True or False where True is white and False is black
self.board = [[True] * width for _ in range(height)]
self.ant_position: tuple[int, int] = (width // 2, height // 2)

# Initially pointing left (similar to the wikipedia image)
# (0 = 0° | 1 = 90° | 2 = 180 ° | 3 = 270°)
self.ant_direction: int = 3

def move_ant(self, axes: plt.Axes | None, display: bool, _frame: int) -> None:
"""
1. The ant turns either clockwise or anti-clockwise according to the colour
of the square that it is currently on. If the square is white, the ant
turns clockwise, and if the square is black the ant turns anti-clockwise
2. The ant moves one square in the direction that it is currently facing
3. The square the ant was previously on is inverted (White -> Black and
Black -> White)

If display is True, the board will also be displayed on the axes

>>> la = LangtonsAnt(2, 2)
>>> la.move_ant(None, True, 0)
>>> la.board
[[True, True], [True, False]]
>>> la.move_ant(None, True, 0)
>>> la.board
[[True, False], [True, False]]
"""
directions = {
0: (-1, 0),  # 0°
1: (0, 1),  # 90°
2: (1, 0),  # 180°
3: (0, -1),  # 270°
}
x, y = self.ant_position

# Turn clockwise or anti-clockwise according to colour of square
if self.board[x][y] is True:
# The square is white so turn 90° clockwise
self.ant_direction = (self.ant_direction + 1) % 4
else:
# The square is black so turn 90° anti-clockwise
self.ant_direction = (self.ant_direction - 1) % 4

# Move ant
move_x, move_y = directions[self.ant_direction]
self.ant_position = (x + move_x, y + move_y)

# Flip colour of square
self.board[x][y] = not self.board[x][y]

if display and axes:
# Display the board on the axes
axes.get_xaxis().set_ticks([])
axes.get_yaxis().set_ticks([])
axes.imshow(self.board, cmap="gray", interpolation="nearest")

def display(self, frames: int = 100_000) -> None:
"""
Displays the board without delay in a matplotlib plot
to visually understand and track the ant.

>>> _ = LangtonsAnt(WIDTH, HEIGHT)
"""
fig, ax = plt.subplots()
# Assign animation to a variable to prevent it from getting garbage collected
self.animation = FuncAnimation(
fig, partial(self.move_ant, ax, True), frames=frames, interval=1
)
plt.show()

if __name__ == "__main__":
import doctest

doctest.testmod()

LangtonsAnt(WIDTH, HEIGHT).display()
```