Asynchronous updating with JCASim

The simulation system JCASim provides the possibility to use customized lattices. This option has been used to create a lattice class (in 2D), which provides ascynchronous updating in the JCASim framework. The asynchrounod updating is used by adding the command line parameters -lc de.tubs.cs.sc.casim.Lattice2DAsync to the invocation of CASimFrame, or by including the following line in the HTML configuration file: 
<param name="latticeclass" value="de.tubs.cs.sc.casim.Lattice2DAsync">
<param name="latticeoption" value="5">
The asynchronous updating can be used with any 2-D cellular automaton rule.

Sequences for updating

There are several possibilities for selecting a sequence for updating the cells. These are discussed in detail in Schönfisch, B. and de Roos, A. : Synchronous and asynchronous updating in cellular automata. BioSystems 51, 123-143, 1999. In the class Lattice2DAsync, five different methods are implemented. These are selected by setting the parameter latticeoption in the configuration file, or in the Lattice-dialog.


1. Line-by-line updating

This option, which uses the line-by line updating also used in the normal CA operation, but without the use of a backup to store the previous state of a cell, produces asymmetric results.

2. Fixed Random Sequence

Using a permutation of the cells which is fixed for all time steps leads to a simulation with more isotropy, but cycling behaviour.

3. Random Sequence

Using a different permutation at each step leads to a simulation with more isotropy and without cycling behaviour. Every cell (of N) is updated exactly onece per time step.

4. Uniform selection

At each time steps, N updates are performed, selecting a cell at random at each step. Some cells may be updated more than once, some not at all during one time step.

5. Exponential Waiting Time

Each cell is assigned a waiting time till the next update that is drawn from an exponential distribution. Cells are then updated in time sequence. During one time step, approximately N cell updates are performed, since the average waiting time is 1.

Applet

Try the different updating methods using this applet: set a new number in the "Lattice option" field of the Lattice dialog to change the updating method.

Applet with a 5-state Greenberg-Hasting rule

Comparison: Synchronous updating with reduced probability

For comparison, try a modified CA, which is fully synchronous, but where each cell is only updated with a certain probability. You can select the probability by changing the value for the "Initial Option" in the Lattice-dialog to a number between 0 and 100, the probability in percent.


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J.Weimar@tu-bs.de 7.11.2000