Seeking advice on trying to read a moore neighbourhood for a 2D cellular automata in MATLAB for an epidemic simulator

Question

I'm currently working on a code that makes use of a 2D cellular automata as an epidemic simulator in MATLAB. The main basic rule I'm trying to implement is that if any neighbour within a Moore Neighbourhood with a 1-cell radius is infected, the cell will become infected. But I can't seem to get a good code working for it.

Basically what I'm trying to do is say with for a cell with a one cell radius Moore neighbourhood, if any values in this neighbourhood = 2, then the initial cell will become 2.

I've tried using the forest fire code on the rosetta code as a basis for my code behaviour but it doesnt work very well. The rules don't really work that well when applying it to mine. I've tried using the mod function and a series of if loops to attach. I'll put in some code of each to give context.

This example doesn't really function well as an epidemic simulator to be honest.

    matlab
    clear; clc;
    n = 200;
    N = n/2;
    E = 0.001; % Creating an arbitrary number for population exposed to                 
                 the disease but not infected
    p = 1 + (rand(n,n)<E);
    %p = ceil(rand(n,n)*2.12) - 1;
    % ratio0 = sum(p(:)==0)/n^2;
    % ratio1 = sum(p(:)==1)/n^2;
    % ratio2 = sum(p(:)==2)/n^2;
    % ratio3 = sum(p(:)==3)/n^2;
    S = ones(3); S(2,2) = 0;
    ff = 0.00000000002;
    p(N,N) = 3;
    %% Running the simulation for a set number of loops
    colormap([1,1,1;1,0,1;1,0,0]); %Setting colourmap to Green, red and 
    grey
    count = 0;
    while(count<365) % Running the simulation with limited number of runs
    count = count + 1;
    image(p); pause(0.1); % Creating an image of the model
    P = (p==1); % Adding empty cells to new array
    P = P + (p==2).*((filter2(S,p==3)>0) + (rand(n,n)<ff) + 2); % Setting         
              2 as a tree, ignites based on proximity of trees and random 
              chance ff
    P = P + (p==3); % Setting 3 as a burning tree, that becomes 1,
    p = P;
    end

second idea. this basically returns nothing

    matlab
    clear;clf;clc;
    n = 200;
    pos = mod((1:n),n) + 1; neg = mod((1:n)-2,n) + 1;
    p = (ceil(rand(n,n)*1.0005));
    for t = 1:365
        if p(neg,neg) ==2 
           p(:,:) = 2;
        end
        if p(:,neg)==2 
           p(:,:) = 2;
        end
        if p(pos,neg)==2
           p(:,:) = 2;
        end
        if p(neg,:)==2
           p(:,:) = 2;
        end   
        if p(pos,:)==2
           p(:,:) = 2;
        end
        if p(neg,pos)==2
           p(:,:) = 2;
        end
        if p(:,pos)==2
           p(:,:) = 2;
        end
        if p(pos,pos)== 2
           p(:,:) = 2;
        end
        image(p)
        colormap([1,1,1;1,0,1])
    end

third I tried using logic gates to see if that would work. I don't know if commas would work instead.

    matlab
    clear;clf;clc;
    n = 200;
    pos = mod((1:n),n) + 1; neg = mod((1:n)-2,n) + 1;
    p = (ceil(rand(n,n)*1.0005));
    %P = p(neg,neg) + p(:,neg) + p(pos,neg) + p(neg,:) + p(:,:) + p(pos,:)         
       + p(neg,pos) + p(:,pos) + p(pos,pos)

    for t=1:365
        if p(neg,neg)|| p(:,neg) || p(pos,neg) || p(neg,:) ||  p(pos,:) ||         
           p(neg,pos) || p(:,pos) || p(pos,pos) == 2
           p(:,:) = 2;
        end
        image(p)
        colormap([1,1,1;1,0,1])
    end

I expected the matrix to just gradually become more magenta but nothing happens in the second one. I get this error for the third.

"Operands to the || and && operators must be convertible to logical scalar values."

I just have no idea what to do!

Answer 1

Cells do not heal

I assume that

• Infected is 2, non-infected is 1;
• An infected cell remains infected;
• A non-infected cell becomes infected if any neighbour is.

A simple way to achieve this is using 2-D convolution:

n = 200;
p = (ceil(rand(n,n)*1.0005));
neighbourhood = [1 1 1; 1 1 1; 1 1 1]; % Moore plus own cell
for t = 1:356
    p = (conv2(p-1, neighbourhood, 'same')>0) + 1; % update
    image(p), axis equal, axis tight, colormap([.4 .4 .5; .8 0 0]), pause(.1) % plot
end

Cells heal after a specified time

• To model this, it is better to use 0 for a non-infected cell and a positive integer for an infected cell, which indicated how long it has been infected.
• A cell heals after it has been infected for a specified number of iterations (but can immediately become infeced again...)

The code uses convolution, as the previous one, but now already infected cells need to be dealt with separately from newly infected cells, and so a true Moore neighbourhood is used.

n = 200;
p = (ceil(rand(n,n)*1.0005))-1; % 0: non-infected. 1: just infected
T = 20; % time to heal
neighbourhood = [1 1 1; 1 0 1; 1 1 1]; % Moore
for t = 1:356    
    already_infected = p>0; % logical index
    p(already_infected) = p(already_infected)+1; % increase time count for infected
    newly_infected = conv2(p>0, neighbourhood, 'same')>0; % logical index
    p(newly_infected & ~already_infected) = 1; % these just became infected
    newly_healed = p==T; % logical index
    p(newly_healed) = 0; % these are just healed
    image(p>0), axis equal, axis tight, colormap([.4 .4 .5; .8 0 0]), pause(.1) % plot
    % infected / non-infected state
end