Wa Tor
A
"""
Wa-Tor algorithm (1984)
@ https://en.wikipedia.org/wiki/Wa-Tor
@ https://beltoforion.de/en/wator/
@ https://beltoforion.de/en/wator/images/wator_medium.webm
This solution aims to completely remove any systematic approach
to the Wa-Tor planet, and utilise fully random methods.
The constants are a working set that allows the Wa-Tor planet
to result in one of the three possible results.
"""
from collections.abc import Callable
from random import randint, shuffle
from time import sleep
from typing import Literal
WIDTH = 50 # Width of the Wa-Tor planet
HEIGHT = 50 # Height of the Wa-Tor planet
PREY_INITIAL_COUNT = 30 # The initial number of prey entities
PREY_REPRODUCTION_TIME = 5 # The chronons before reproducing
PREDATOR_INITIAL_COUNT = 50 # The initial number of predator entities
# The initial energy value of predator entities
PREDATOR_INITIAL_ENERGY_VALUE = 15
# The energy value provided when consuming prey
PREDATOR_FOOD_VALUE = 5
PREDATOR_REPRODUCTION_TIME = 20 # The chronons before reproducing
MAX_ENTITIES = 500 # The max number of organisms on the board
# The number of entities to delete from the unbalanced side
DELETE_UNBALANCED_ENTITIES = 50
class Entity:
"""
Represents an entity (either prey or predator).
>>> e = Entity(True, coords=(0, 0))
>>> e.prey
True
>>> e.coords
(0, 0)
>>> e.alive
True
"""
def __init__(self, prey: bool, coords: tuple[int, int]) -> None:
self.prey = prey
# The (row, col) pos of the entity
self.coords = coords
self.remaining_reproduction_time = (
PREY_REPRODUCTION_TIME if prey else PREDATOR_REPRODUCTION_TIME
)
self.energy_value = None if prey is True else PREDATOR_INITIAL_ENERGY_VALUE
self.alive = True
def reset_reproduction_time(self) -> None:
"""
>>> e = Entity(True, coords=(0, 0))
>>> e.reset_reproduction_time()
>>> e.remaining_reproduction_time == PREY_REPRODUCTION_TIME
True
>>> e = Entity(False, coords=(0, 0))
>>> e.reset_reproduction_time()
>>> e.remaining_reproduction_time == PREDATOR_REPRODUCTION_TIME
True
"""
self.remaining_reproduction_time = (
PREY_REPRODUCTION_TIME if self.prey is True else PREDATOR_REPRODUCTION_TIME
)
def __repr__(self) -> str:
"""
>>> Entity(prey=True, coords=(1, 1))
Entity(prey=True, coords=(1, 1), remaining_reproduction_time=5)
>>> Entity(prey=False, coords=(2, 1)) # doctest: +NORMALIZE_WHITESPACE
Entity(prey=False, coords=(2, 1),
remaining_reproduction_time=20, energy_value=15)
"""
repr_ = (
f"Entity(prey={self.prey}, coords={self.coords}, "
f"remaining_reproduction_time={self.remaining_reproduction_time}"
)
if self.energy_value is not None:
repr_ += f", energy_value={self.energy_value}"
return f"{repr_})"
class WaTor:
"""
Represents the main Wa-Tor algorithm.
:attr time_passed: A function that is called every time
time passes (a chronon) in order to visually display
the new Wa-Tor planet. The time_passed function can block
using time.sleep to slow the algorithm progression.
>>> wt = WaTor(10, 15)
>>> wt.width
10
>>> wt.height
15
>>> len(wt.planet)
15
>>> len(wt.planet[0])
10
>>> len(wt.get_entities()) == PREDATOR_INITIAL_COUNT + PREY_INITIAL_COUNT
True
"""
time_passed: Callable[["WaTor", int], None] | None
def __init__(self, width: int, height: int) -> None:
self.width = width
self.height = height
self.time_passed = None
self.planet: list[list[Entity | None]] = [[None] * width for _ in range(height)]
# Populate planet with predators and prey randomly
for _ in range(PREY_INITIAL_COUNT):
self.add_entity(prey=True)
for _ in range(PREDATOR_INITIAL_COUNT):
self.add_entity(prey=False)
self.set_planet(self.planet)
def set_planet(self, planet: list[list[Entity | None]]) -> None:
"""
Ease of access for testing
>>> wt = WaTor(WIDTH, HEIGHT)
>>> planet = [
... [None, None, None],
... [None, Entity(True, coords=(1, 1)), None]
... ]
>>> wt.set_planet(planet)
>>> wt.planet == planet
True
>>> wt.width
3
>>> wt.height
2
"""
self.planet = planet
self.width = len(planet[0])
self.height = len(planet)
def add_entity(self, prey: bool) -> None:
"""
Adds an entity, making sure the entity does
not override another entity
>>> wt = WaTor(WIDTH, HEIGHT)
>>> wt.set_planet([[None, None], [None, None]])
>>> wt.add_entity(True)
>>> len(wt.get_entities())
1
>>> wt.add_entity(False)
>>> len(wt.get_entities())
2
"""
while True:
row, col = randint(0, self.height - 1), randint(0, self.width - 1)
if self.planet[row][col] is None:
self.planet[row][col] = Entity(prey=prey, coords=(row, col))
return
def get_entities(self) -> list[Entity]:
"""
Returns a list of all the entities within the planet.
>>> wt = WaTor(WIDTH, HEIGHT)
>>> len(wt.get_entities()) == PREDATOR_INITIAL_COUNT + PREY_INITIAL_COUNT
True
"""
return [entity for column in self.planet for entity in column if entity]
def balance_predators_and_prey(self) -> None:
"""
Balances predators and preys so that prey
can not dominate the predators, blocking up
space for them to reproduce.
>>> wt = WaTor(WIDTH, HEIGHT)
>>> for i in range(2000):
... row, col = i // HEIGHT, i % WIDTH
... wt.planet[row][col] = Entity(True, coords=(row, col))
>>> entities = len(wt.get_entities())
>>> wt.balance_predators_and_prey()
>>> len(wt.get_entities()) == entities
False
"""
entities = self.get_entities()
shuffle(entities)
if len(entities) >= MAX_ENTITIES - MAX_ENTITIES / 10:
prey = [entity for entity in entities if entity.prey]
predators = [entity for entity in entities if not entity.prey]
prey_count, predator_count = len(prey), len(predators)
entities_to_purge = (
prey[:DELETE_UNBALANCED_ENTITIES]
if prey_count > predator_count
else predators[:DELETE_UNBALANCED_ENTITIES]
)
for entity in entities_to_purge:
self.planet[entity.coords[0]][entity.coords[1]] = None
def get_surrounding_prey(self, entity: Entity) -> list[Entity]:
"""
Returns all the prey entities around (N, S, E, W) a predator entity.
Subtly different to the try_to_move_to_unoccupied square.
>>> wt = WaTor(WIDTH, HEIGHT)
>>> wt.set_planet([
... [None, Entity(True, (0, 1)), None],
... [None, Entity(False, (1, 1)), None],
... [None, Entity(True, (2, 1)), None]])
>>> wt.get_surrounding_prey(
... Entity(False, (1, 1))) # doctest: +NORMALIZE_WHITESPACE
[Entity(prey=True, coords=(0, 1), remaining_reproduction_time=5),
Entity(prey=True, coords=(2, 1), remaining_reproduction_time=5)]
>>> wt.set_planet([[Entity(False, (0, 0))]])
>>> wt.get_surrounding_prey(Entity(False, (0, 0)))
[]
>>> wt.set_planet([
... [Entity(True, (0, 0)), Entity(False, (1, 0)), Entity(False, (2, 0))],
... [None, Entity(False, (1, 1)), Entity(True, (2, 1))],
... [None, None, None]])
>>> wt.get_surrounding_prey(Entity(False, (1, 0)))
[Entity(prey=True, coords=(0, 0), remaining_reproduction_time=5)]
"""
row, col = entity.coords
adjacent: list[tuple[int, int]] = [
(row - 1, col), # North
(row + 1, col), # South
(row, col - 1), # West
(row, col + 1), # East
]
return [
ent
for r, c in adjacent
if 0 <= r < self.height
and 0 <= c < self.width
and (ent := self.planet[r][c]) is not None
and ent.prey
]
def move_and_reproduce(
self, entity: Entity, direction_orders: list[Literal["N", "E", "S", "W"]]
) -> None:
"""
Attempts to move to an unoccupied neighbouring square
in either of the four directions (North, South, East, West).
If the move was successful and the remaining_reproduction time is
equal to 0, then a new prey or predator can also be created
in the previous square.
:param direction_orders: Ordered list (like priority queue) depicting
order to attempt to move. Removes any systematic
approach of checking neighbouring squares.
>>> planet = [
... [None, None, None],
... [None, Entity(True, coords=(1, 1)), None],
... [None, None, None]
... ]
>>> wt = WaTor(WIDTH, HEIGHT)
>>> wt.set_planet(planet)
>>> wt.move_and_reproduce(Entity(True, coords=(1, 1)), direction_orders=["N"])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[None, Entity(prey=True, coords=(0, 1), remaining_reproduction_time=4), None],
[None, None, None],
[None, None, None]]
>>> wt.planet[0][0] = Entity(True, coords=(0, 0))
>>> wt.move_and_reproduce(Entity(True, coords=(0, 1)),
... direction_orders=["N", "W", "E", "S"])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[Entity(prey=True, coords=(0, 0), remaining_reproduction_time=5), None,
Entity(prey=True, coords=(0, 2), remaining_reproduction_time=4)],
[None, None, None],
[None, None, None]]
>>> wt.planet[0][1] = wt.planet[0][2]
>>> wt.planet[0][2] = None
>>> wt.move_and_reproduce(Entity(True, coords=(0, 1)),
... direction_orders=["N", "W", "S", "E"])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[Entity(prey=True, coords=(0, 0), remaining_reproduction_time=5), None, None],
[None, Entity(prey=True, coords=(1, 1), remaining_reproduction_time=4), None],
[None, None, None]]
>>> wt = WaTor(WIDTH, HEIGHT)
>>> reproducable_entity = Entity(False, coords=(0, 1))
>>> reproducable_entity.remaining_reproduction_time = 0
>>> wt.planet = [[None, reproducable_entity]]
>>> wt.move_and_reproduce(reproducable_entity,
... direction_orders=["N", "W", "S", "E"])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[Entity(prey=False, coords=(0, 0),
remaining_reproduction_time=20, energy_value=15),
Entity(prey=False, coords=(0, 1), remaining_reproduction_time=20,
energy_value=15)]]
"""
row, col = coords = entity.coords
adjacent_squares: dict[Literal["N", "E", "S", "W"], tuple[int, int]] = {
"N": (row - 1, col), # North
"S": (row + 1, col), # South
"W": (row, col - 1), # West
"E": (row, col + 1), # East
}
# Weight adjacent locations
adjacent: list[tuple[int, int]] = []
for order in direction_orders:
adjacent.append(adjacent_squares[order])
for r, c in adjacent:
if (
0 <= r < self.height
and 0 <= c < self.width
and self.planet[r][c] is None
):
# Move entity to empty adjacent square
self.planet[r][c] = entity
self.planet[row][col] = None
entity.coords = (r, c)
break
# (2.) See if it possible to reproduce in previous square
if coords != entity.coords and entity.remaining_reproduction_time <= 0:
# Check if the entities on the planet is less than the max limit
if len(self.get_entities()) < MAX_ENTITIES:
# Reproduce in previous square
self.planet[row][col] = Entity(prey=entity.prey, coords=coords)
entity.reset_reproduction_time()
else:
entity.remaining_reproduction_time -= 1
def perform_prey_actions(
self, entity: Entity, direction_orders: list[Literal["N", "E", "S", "W"]]
) -> None:
"""
Performs the actions for a prey entity
For prey the rules are:
1. At each chronon, a prey moves randomly to one of the adjacent unoccupied
squares. If there are no free squares, no movement takes place.
2. Once a prey has survived a certain number of chronons it may reproduce.
This is done as it moves to a neighbouring square,
leaving behind a new prey in its old position.
Its reproduction time is also reset to zero.
>>> wt = WaTor(WIDTH, HEIGHT)
>>> reproducable_entity = Entity(True, coords=(0, 1))
>>> reproducable_entity.remaining_reproduction_time = 0
>>> wt.planet = [[None, reproducable_entity]]
>>> wt.perform_prey_actions(reproducable_entity,
... direction_orders=["N", "W", "S", "E"])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[Entity(prey=True, coords=(0, 0), remaining_reproduction_time=5),
Entity(prey=True, coords=(0, 1), remaining_reproduction_time=5)]]
"""
self.move_and_reproduce(entity, direction_orders)
def perform_predator_actions(
self,
entity: Entity,
occupied_by_prey_coords: tuple[int, int] | None,
direction_orders: list[Literal["N", "E", "S", "W"]],
) -> None:
"""
Performs the actions for a predator entity
:param occupied_by_prey_coords: Move to this location if there is prey there
For predators the rules are:
1. At each chronon, a predator moves randomly to an adjacent square occupied
by a prey. If there is none, the predator moves to a random adjacent
unoccupied square. If there are no free squares, no movement takes place.
2. At each chronon, each predator is deprived of a unit of energy.
3. Upon reaching zero energy, a predator dies.
4. If a predator moves to a square occupied by a prey,
it eats the prey and earns a certain amount of energy.
5. Once a predator has survived a certain number of chronons
it may reproduce in exactly the same way as the prey.
>>> wt = WaTor(WIDTH, HEIGHT)
>>> wt.set_planet([[Entity(True, coords=(0, 0)), Entity(False, coords=(0, 1))]])
>>> wt.perform_predator_actions(Entity(False, coords=(0, 1)), (0, 0), [])
>>> wt.planet # doctest: +NORMALIZE_WHITESPACE
[[Entity(prey=False, coords=(0, 0),
remaining_reproduction_time=20, energy_value=19), None]]
"""
assert entity.energy_value is not None # [type checking]
# (3.) If the entity has 0 energy, it will die
if entity.energy_value == 0:
self.planet[entity.coords[0]][entity.coords[1]] = None
return
# (1.) Move to entity if possible
if occupied_by_prey_coords is not None:
# Kill the prey
prey = self.planet[occupied_by_prey_coords[0]][occupied_by_prey_coords[1]]
assert prey is not None
prey.alive = False
# Move onto prey
self.planet[occupied_by_prey_coords[0]][occupied_by_prey_coords[1]] = entity
self.planet[entity.coords[0]][entity.coords[1]] = None
entity.coords = occupied_by_prey_coords
# (4.) Eats the prey and earns energy
entity.energy_value += PREDATOR_FOOD_VALUE
else:
# (5.) If it has survived the certain number of chronons it will also
# reproduce in this function
self.move_and_reproduce(entity, direction_orders)
# (2.) Each chronon, the predator is deprived of a unit of energy
entity.energy_value -= 1
def run(self, *, iteration_count: int) -> None:
"""
Emulate time passing by looping iteration_count times
>>> wt = WaTor(WIDTH, HEIGHT)
>>> wt.run(iteration_count=PREDATOR_INITIAL_ENERGY_VALUE - 1)
>>> len(list(filter(lambda entity: entity.prey is False,
... wt.get_entities()))) >= PREDATOR_INITIAL_COUNT
True
"""
for iter_num in range(iteration_count):
# Generate list of all entities in order to randomly
# pop an entity at a time to simulate true randomness
# This removes the systematic approach of iterating
# through each entity width by height
all_entities = self.get_entities()
for __ in range(len(all_entities)):
entity = all_entities.pop(randint(0, len(all_entities) - 1))
if entity.alive is False:
continue
directions: list[Literal["N", "E", "S", "W"]] = ["N", "E", "S", "W"]
shuffle(directions) # Randomly shuffle directions
if entity.prey:
self.perform_prey_actions(entity, directions)
else:
# Create list of surrounding prey
surrounding_prey = self.get_surrounding_prey(entity)
surrounding_prey_coords = None
if surrounding_prey:
# Again, randomly shuffle directions
shuffle(surrounding_prey)
surrounding_prey_coords = surrounding_prey[0].coords
self.perform_predator_actions(
entity, surrounding_prey_coords, directions
)
# Balance out the predators and prey
self.balance_predators_and_prey()
if self.time_passed is not None:
# Call time_passed function for Wa-Tor planet
# visualisation in a terminal or a graph.
self.time_passed(self, iter_num)
def visualise(wt: WaTor, iter_number: int, *, colour: bool = True) -> None:
"""
Visually displays the Wa-Tor planet using
an ascii code in terminal to clear and re-print
the Wa-Tor planet at intervals.
Uses ascii colour codes to colourfully display
the predators and prey.
(0x60f197) Prey = #
(0xfffff) Predator = x
>>> wt = WaTor(30, 30)
>>> wt.set_planet([
... [Entity(True, coords=(0, 0)), Entity(False, coords=(0, 1)), None],
... [Entity(False, coords=(1, 0)), None, Entity(False, coords=(1, 2))],
... [None, Entity(True, coords=(2, 1)), None]
... ])
>>> visualise(wt, 0, colour=False) # doctest: +NORMALIZE_WHITESPACE
# x .
x . x
. # .
<BLANKLINE>
Iteration: 0 | Prey count: 2 | Predator count: 3 |
"""
if colour:
__import__("os").system("")
print("\x1b[0;0H\x1b[2J\x1b[?25l")
reprint = "\x1b[0;0H" if colour else ""
ansi_colour_end = "\x1b[0m " if colour else " "
planet = wt.planet
output = ""
# Iterate over every entity in the planet
for row in planet:
for entity in row:
if entity is None:
output += " . "
else:
if colour is True:
output += (
"\x1b[38;2;96;241;151m"
if entity.prey
else "\x1b[38;2;255;255;15m"
)
output += f" {'#' if entity.prey else 'x'}{ansi_colour_end}"
output += "\n"
entities = wt.get_entities()
prey_count = sum(entity.prey for entity in entities)
print(
f"{output}\n Iteration: {iter_number} | Prey count: {prey_count} | "
f"Predator count: {len(entities) - prey_count} | {reprint}"
)
# Block the thread to be able to visualise seeing the algorithm
sleep(0.05)
if __name__ == "__main__":
import doctest
doctest.testmod()
wt = WaTor(WIDTH, HEIGHT)
wt.time_passed = visualise
wt.run(iteration_count=100_000)
