Create langtons ant algorithm (TheAlgorithms#8967)

* updating DIRECTORY.md

* feat(cellular_automata): Langonts ant algorithm

* updating DIRECTORY.md

* Update cellular_automata/langtons_ant.py

Co-authored-by: Tianyi Zheng <[email protected]>

* Apply suggestions from code review

Co-authored-by: Tianyi Zheng <[email protected]>

* fix(langtons-ant): Set funcanimation interval to 1

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <[email protected]>

Author: 3 people

Diff for: DIRECTORY.md

@@ -72,6 +72,7 @@
 ## Cellular Automata
   * [Conways Game Of Life](cellular_automata/conways_game_of_life.py)
   * [Game Of Life](cellular_automata/game_of_life.py)
+  * [Langtons Ant](cellular_automata/langtons_ant.py)
   * [Nagel Schrekenberg](cellular_automata/nagel_schrekenberg.py)
   * [One Dimensional](cellular_automata/one_dimensional.py)
   * [Wa Tor](cellular_automata/wa_tor.py)

Diff for: cellular_automata/langtons_ant.py

@@ -0,0 +1,106 @@
+"""
+Langton's ant
+
+@ https://en.wikipedia.org/wiki/Langton%27s_ant
+@ https://upload.wikimedia.org/wikipedia/commons/0/09/LangtonsAntAnimated.gif
+"""
+
+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 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:
+        """
+        Performs three tasks:
+            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()