A framework for gridded simulations in Julia
Author cesaraustralia
19 Stars
Updated Last
9 Months Ago
Started In
June 2018


Build Status codecov.io

DynamicGrids is a generalised framework for building high-performance grid-based spatial models, including celluar automata, but also allowing arbitrary behviours such as long distance jumps and interactions between multiple grids. It is extended by Dispersal.jl for modelling organism dispersal processes.

Dispersal quarantine

A dispersal simulation with quarantine interactions, using Dispersal.jl, custom rules and the GtkOuput from DynamicGridsGtk. Note that this is indicative of the real-time frame-rate on a laptop.

A DynamicGrids.jl simulation is run with a script like this one running the included game of life model Life():

using DynamicGrids, Crayons

init = rand(Bool, 150, 200)
output = REPLOutput(init; tspan=1:200, fps=30, color=Crayon(foreground=:red, background=:black, bold=true))
sim!(output, Life())

REPL life

A game of life simulation being displayed directly in a terminal.


The framework is highly customisable, but there are some central ideas that define how a simulation works: rules and interactions, init arrays and outputs.


Rules hold the parameters for running a simulation. Each rule triggers a specific applyrule method that operates on each of the active cells in the grid. Rules come in a number of flavours (outlined in the docs), which allow assumptions to be made about running them that can greatly improve performance. Rules are added to a Ruleset, with some additional parameters:

ruleset = Ruleset(Life(2, 3); opt=SparseOpt())

Multiple models can be combined in a Ruleset. Each rule will be run for the whole grid, in sequence, using appropriate optimisations depending on the parent types of each rule:

ruleset = Ruleset(rule1, rule2; timestep=Day(1), opt=SparseOpt())

For better performance (often ~2x or more), models included in a Chain object will be combined into a single model, using only one array read and write. This optimisation is limited to CellRule, or a NeighborhoodRule followed by CellRule. If the @inline compiler macro is used on all applyrule methods, all rules in a Chain will be compiled together into a single, efficient function call.

ruleset = Ruleset(rule1, Chain(rule2, rule3, rule4))

A Ruleset can hold rules that act on multiple grids. These may either run side by side independently (say for live comparative analysis), or may interact.


init may be any AbstractArray or a NamedTuple of AbstractArray, It contains whatever initialisation data is required to start the simulation. The array type, size and element type of the init object determine the types used in the simulation, as well as providing the initial conditions:

init = rand(Float32, 100, 100)

An init array can be attached to a Ruleset:

ruleset = Ruleset(Life(); init=init)

or passed into a simulation, where it will take preference over the Ruleset init:

sim!(output, rulset; init=init)

For multiple grids, init is a NamedTuple of equal-sized arrays matching the names given to each Ruleset :

init = (predator=rand(100, 100), prey=(rand(100, 100))

Handling and passing of the correct arrays is automated by DynamicGrids.jl. Rules must specify which grids they require in what order, using the first two (R and W) type parameters.

Dimensional or spatial init arrays from DimensionalData.jl of GeoData.jl will propagate through the model to return output with explicit dimensions. This will plot correctly as a map using Plots.jl, to which shape files and observation points can be easily added.


Outputs are ways of storing or viewing a simulation. They can be used interchangeably depending on your needs: ArrayOutput is a simple storage structure for high performance-simulations. As with most outputs, it is initialised with the init array, but in this case it also requires the number of simulation frames to preallocate before the simulation runs.

output = ArrayOutput(init; tspan=1:10)

The REPLOutput shown above is an inbuilt GraphicOutput that can be useful for checking a simulation when working in a terminal or over ssh:

output = REPLOutput(init; tspan=1:100)

ImageOutput is the most complex class of outputs, allowing full color visual simulations using COlorSchemes.jl. It can also display interactions using color composites or layouts, as shown above in the quarantine simulation.

DynamicGridsInteract.jl provides simulation interfaces for use in Juno, Jupyter, web pages or electron apps, with live interactive control over parameters. DynamicGridsGtk.jl is a simple graphical output for Gtk. These packages are kept separate to avoid dependencies when being used in non-graphical simulations.

Outputs are also easy to write, and high performance or applications may benefit from writing a custom output to reduce memory use, such as running a loss function on the fly instead of storing the array. Performance of DynamicGrids.jl is dominated by cache interactions, and reducing memory use has significant positive effects. Custom frame processors can also be written, which can help developing specialised visualisations.


This example implements a very simple forest fire model:

using DynamicGrids, DynamicGridsGtk, ColorSchemes, Colors

const DEAD, ALIVE, BURNING = 1, 2, 3

rule = let prob_combustion=0.0001, prob_regrowth=0.01
    Neighbors(RadialNeighborhood{1}()) do neighborhood, cell
        if cell == ALIVE
            if BURNING in neighborhood
                rand() <= prob_combustion ? BURNING : ALIVE
        elseif cell in BURNING
            rand() <= prob_regrowth ? ALIVE : DEAD

# Set up the init array and output (using a Gtk window)
init = fill(ALIVE, 400, 400)
processor = ColorProcessor(scheme=ColorSchemes.rainbow, zerocolor=RGB24(0.0))
output = GtkOutput(init; tspan=1:200, fps=25, minval=DEAD, maxval=BURNING, processor=processor)

# Run the simulation
sim!(output, rule)

# Save the output as a gif
savegif("forestfire.gif", output)


Timing the simulation for 200 steps, the performance is quite good:

output = ArrayOutput(init; tspan=1:200)
@time sim!(output, ruleset)
 1.384755 seconds (640 allocations: 2.569 MiB)

# To save a gif of the ArrayOutput we need to pass in a processor and the min and max
# values used in the simulation:

savegif("forestfire.gif", output; minval=DEAD, maxval=BURNING, processor=processor)


Agents.jl can also do cellular-automata style simulations. The design of Agents.jl is to iterate over a list of agents, instead of broadcasting over an array of cells. This approach is well suited to when you need to track the movement and details about individual agents throughout the simulation.

However, for simple grid models where you don't need to track individuals, like the forest fire model above, DynamicGrids.jl is two orders of magnitude faster than Agents.jl, and provides better visualisation tools. If you are doing grid-based simulation and you don't need to track individual agents, DynamicGrids.jl is probably the best tool. For other use cases, try Agents.jl.