cavl

cavl is a simple library for simulating and visualizing various cellular automata.

Installation

Install using pip:

pip install cavl

Note: If you want to use the built-in animation functionality, you also need to install ffmpeg.

Usage

cavl provides two main classes for creating and simulating cellular automata: CellularAutomaton1D and CellularAutomaton2D, for 1D and 2D cellular automata respectively.

Both classes take the same number and type of parameters for initialization:

• init: the starting grid for the cellular automata
• neighbors: list of coordinates to represent the neighborhood of a cell
• apply: function to apply a given rule to a single cell (signature depends on whether working with 1D or 2D cellular automata)
  • 1D: takes dictionary with keys as relative coordinates of a neighbor and values representing the current state number of that neighbor (dict[tuple[int, int], float])
  • 2D: takes same dictionary as with 1D apply function, as well as the state number of the current cell being worked on
  • The given apply function should return the state number that the current cell should be in the next generation.

Neighborhoods

cavl provides built-in helper functions for retrieving lists of tuple coordinates representing common neighborhoods.

• moore(radius: int): returns list of tuple[int, int] representing a Moore neighborhood with given radius (default of 1)
  • i.e. moore() returns [(-1, -1), (0, -1), (1, -1), (-1, 0), (1, 0), (-1, 1), (0, 1), (1, 1)]
• von_neumann(radius: int): returns list of tuple[int, int] representing a von Neumann neighborhood with given radius (default of 1)
  • i.e. von_neumann() returns [(0, -1), (-1, 0), (1, 0), (0, 1)]

Visualization

cavl provides several built-in functions for visualizing your cellular automata:

• plot: used to visualize the generations of a 1D cellular automaton
• animate: used to animate the progression of the generations of a 1D cellular automaton
• plot2d: used to visualize the most recent generation of a 2D cellular automaton
• animate2d: used to animate the progression of the generations of a 2D cellular automaton

1D Cellular Automata

Rules

cavl also provides some built-in classes for common cellular automata rules. Currently, there are only two built-in 1D cellular automata rules:

• General1DRule: takes a rule using the Wolfram code naming system
• Totalistic1DRule: rule that looks at the total of the values of the cells in a neighborhood; more information here

Example

import cavl

start = cavl.init(50)  # returns 1D array with width of 50

rule = cavl.General1DRule(30)

automaton = cavl.CellularAutomaton1D(init=start, neighbors=rule.neighbors, apply=rule.apply)
automaton.evolve(20)

cavl.plot(automaton, save=True, filename='1D_automaton')

2D Cellular Automata

Rules

Currently, there are no built-in rule classes that work with 2D cellular automata; some will be added later on.

Example

import cavl

# simple period 2 oscillator
start = [[0, 0, 0, 0, 0, 0, 0, 0],
         [0, 0, 0, 0, 0, 0, 0, 0],
         [0, 0, 0, 0, 0, 0, 0, 0],
         [0, 0, 0, 1, 1, 1, 0, 0],
         [0, 0, 1, 1, 1, 0, 0, 0],
         [0, 0, 0, 0, 0, 0, 0, 0],
         [0, 0, 0, 0, 0, 0, 0, 0],
         [0, 0, 0, 0, 0, 0, 0, 0]]

neighbors = cavl.moore()

# Conway's Game of Life rules
def apply(neighbors, current) -> int:
    alive = sum(neighbors.values())
    if current == 1 and (alive == 2 or alive == 3):
        return 1
    elif current == 0 and alive == 3:
        return 1
    else:
        return 0


automaton = cavl.CellularAutomaton2D(init=start, neighbors=neighbors, apply=apply)
automaton.evolve(21)

cavl.plot2d(automaton, save=True, filename='2D_automaton')

TODO

• More built-in rules
  • Cyclic
  • Life-like
• Additional grid layouts
  • Hexagonal
  • Triangular
• ...and more