Morpheus

This example models probably the best-known classic cellular automaton (CA) model: Conway's Game of Life.

It shows an alternative use of System for synchronous updating of Equations.

In this model, the lattice is filled with cells of size 1. Each cell counts the number of neighboring cells that are 'alive' and acts accordingly. The rules that make up the Game of Life are implemented in a System of Equations in which all Equations are updated synchronously.

• Change the Neighborhood from a Moore (2nd order) to von Neumann (1st order).

This example shows Wolpert's classical French Flag model. Depending on the local concentration of a morphogen, cells adopt one of three cell types based on internal thresholds.

The model sets up a morphogen gradient in the x direction PDE. Note that no diffusion is used, since we use the steady-state solution of diffusion.

The cells in CellType register the (average) local morphogen concentration using PDEReporter. Based on the specified threshold values, they choose an identity I as defined in the Equation.

Note that this model is not time-dependent. Time is therefore set from StartTime 0 to StopTime 0.

• Change the physical length of the domain by editing Space → NodeLength that controls the physical size per lattice site.
• Change the model such that the morphogen gradient is set up by production and diffusion, using Diffusion and a System with DiffEqn. That is, change the model into a time-dependent model.

This models approximates an interacting particle system (IPS) model of particle aggregation. Each black dot represents a particle that moved due to spin flips with random neighbors. The particles perform random walks in which the probability of moving depends on the number of neighboring cells.

Each lattice site (white or black) counts the number of particles (black neighboring sites) using a NeighborsReporter.

The probability of movement of each particle is made dependent on its number of neighbors by using it in the Condition of FlipCells. When this condition is satisfied, the particle changes positions with a random neighboring lattice site.

A PopulationReporter is used to return the fraction of isolated black particles. This number is logged and plotted using the Logger.

• Change the parameter p.