Conway’s GameOfLife#

This model implements Conway’s Game of Life as well as all two-dimensional life-like cellular automata. For information on the model and its generalization to two-dimensional rules, please have a look at the linked Wikipedia articles and, if needed, follow the references presented in the articles.

Default Model Configuration#

Below are the default configuration parameters for the GameOfLife model:

# --- Space parameters
# The physical space this model is embedded in
space:
  periodic: true

# --- CellManager and cell initialization
cell_manager:
  grid:
    structure: square
    resolution: 128      # in cells per unit length of physical space

  neighborhood:
    mode: Moore

# --- Initialization 
# Initialize cells that should be set to living.
# This feature uses the `select_entities` interface; consult the
# documentation regarding information on available selection modes.
# Turn dead cells into living cells. All cells that do not fulfill the 
# condition are set to be dead.
living:
  mode: probability

  # Probability parameter
  probability: 0.1

  # Clustering parameters
  p_seed: .02            # Probability with which a cell is a cluster seed
  p_attach: .1           # Attachment probability (per neighbor)
  num_passes: 5          # How many attachment procedures to perform

# --- Rule specification
# Specify a rule in the notation used by Mirek's Cellebration as a string in
# in form `x/y` with:
#   - `x`: The number of neighbors required for a cell to get born
#   - `y`: The number of neighbors required to survive
# In this notation, the game of life is given as `3/23`
rule: 3/23

Available Plots#

The following plot configurations are available for the GameOfLife model:

Default Plot Configuration#

# Plot the density time development of living cells
living_density:
  based_on: density_living_cells

# Plot an animation of the cellular automaton
CA_state_anim:
  based_on:
    - state_anim
    - .ca.state.anim_ffmpeg 
  to_plot:
    living:
      title: Living

Base Plot Configuration#

# Plot a state animation of the cellular automaton
state_anim:
  based_on: .ca.state

  model_name: GameOfLife

  # Specify the time index (will be ignored, but needs to be specified)
  time_idx: 0

  # Enable animation
  animation:
    enabled: true

# Plot the mean density of living cells
density_living_cells:
  based_on: .dag.generic.facet_grid
  creator: multiverse

  select_and_combine:
    fields:
      living: living
    base_path: data/GameOfLife

  transform:
    # The 'data' provided to the facet_grid plot function is the mean over
    # the 'x' and 'y' dimension. Due to the fact that living is represented as
    # 1 and dead as 0, calculating the mean over all grid cells automatically
    # results in the density
    - operation: .mean
      args: [!dag_tag living, ['x', 'y']]
      tag: data

For the utopya base plots, see Multiverse Base Configuration.

Possible Future Extensions#

This model can be expanded in many different ways. A few ideas are:

  • Expand the initialization options to position well-known structures such as gliders or space-ships at desired locations on the grid.

  • Introduce stochasticity into the model by introducing birth and/or death probabilities. For these cases, also provide means to plot and analyze the data.

References#