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Cellular Automata Examples
The applet on this page is a simple Greenburg Hastings type cellular automaton (CA).
In a CA, each cell has a finite number of states, which
are updated based on its neighbours and its own state the previous time step. In CA models
of cardiac dynamics, the cells are either active, refractory or excitable. The length
of time each cell spends in each state, as well as the size of the neighbourhood and the
threshold for activation, are all adjustable parameters. A similar model is formally described here.
Spiral waves.
Spirals have different characteristics for
different parameters. Control-click in the window to bring up a graph that shows the period
of the spiral.
RUN Neighbourhood=1, E=8, R=10, threshold=3
RUN Neighbourhood=1, E=5, R=6, threshold=2
RUN Neighbourhood=3, E=5, R=6, threshold=14
RUN Neighbourhood=5, E=10, R=11, threshold=38
Noise.
Inactive cells have a small chance of becoming active in this example. This activity
can cause unidirectional propagation
and spiral waves. (A periodic target
wave is included to show the effects of noise on wave propagation in the second example.)
RUN Neighbourhood=1, E=5, R=6, threshold=3
RUN Neighbourhood=2, E=5, R=6, threshold=6
Periodic pacing with ECG.
A target wave is initiated every 100 timesteps from
the top left corner. A reconstructed 'ECG' (Davidenko et al.Circ Res. 1995,77(6):1166-79) is displayed in a seperate window. You can start a target wave
if you click in the applet, and you can get a spiral wave by clicking in the wake of the periodic wave.
parameters:
Neighbourhood size=2, threshold=6, E=3, R=6.
RUN
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reset |
start |
stop
To adjust all the parameters seperately, click here
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Click in the simulation to start a target wave.
Control-Clicking in the simulation to bring up a chart that shows the period of the
spiral at that point. (Doing this several times allows you to check the period at different points.)
Dragging the mouse in the chart window rescales and moves each chart. The charts can be selected by clicking
on the appropriate square in the rightmost window.
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Some other projects that integrate mathematics and biology are listed on our MITACS project site.
Also, check out some of the great resources from other instutions, such as J. Weimar's cellular automaton lectures. They are listed
in the links page.
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