(mainly refer to the teaching video of zhou lvwen)
Cellular automata is a discrete dynamic system, which is defined in a finite time space and has a finite number of cells
Mathematical expression A=(L,d,s,N,f)
50: Cell grid space
d: Space dimension
s: Finite set of discrete states (for example, 0, 1)
N: The possibility of all cells in a neighborhood
f: Local mapping or local rules
Cell is its basic unit, each of which has the function of memorizing and storing state
Several different neighborhood relationships

Boundary conditions: periodic type, constant value type, absorption type, reflection type
Rules:
Summation: look at the total state of neighbors
Legal type:
Example: forest fire

Code

% simulate forest fire with cellular automata
n = 300;%Definition represents forest matrix size
Plight = 5e-6; %Lightning probability
Pgrowth = 1e-2;%Probability of tree growth
UL = [n 1:n-1]; %Upper left neighbor processing
DR = [2:n 1];
veg=zeros(n,n);%Initialization matrix
imh = image(cat(3,veg,veg,veg));%Visualization ( R，G，B Three level matrix)
% veg = empty=0 burning=1 green=2 Three different states
for i=1:3000%Loop start
    %nearby fires?
    sum =            (veg(UL,:)==1) + ...
        (veg(:,UL)==1)     +      (veg(:,DR)==1) + ...
                     (veg(DR,:)==1);%Four neighbors up and down
                 %Updating forest matrix according to rules: tree=total-Catch fire+newborn

    veg = 2*(veg==2) - ...
          ( (veg==2) & (sum>0 | (rand(n,n)<Plight)) ) + ...
          2*((veg==0) & rand(n,n)<Pgrowth) ;
     
    set(imh, 'cdata', cat(3,(veg==1),(veg==2),zeros(n)) )%visualization
    drawnow
end

Example: monorail problems
Code

function [rho, flux, vmean] = ns(rho, p, L, tmax, animation, spacetime)
%
% NS: This script implements the Nagel Schreckenberg cellular automata based
% traffic model. Car move forward governed by NS algorithm:
% USAGE: flux = ns(rho, p, L, tmax, isdraw)
%        rho       = density of the traffic Density is p(rou)
%        p         = probability of random braking Random deceleration probability
%        L         = length of the load
%        tmax      = number of the iterations Time step
%        animation = if show the animation of the traffic
%        spacetime = if plot the space-time after the simuation ended.
%        flux      = flux of the traffic
%


if nargin == 0; 
    rho = 0.25; p = 0.25; L = 100; tmax = 100; 
    animation = true; spacetime = true;
end

vmax = 5;                  % maximun speed
% place a distribution with density
ncar = round(L*rho);%ncar=L*rho
rho = ncar/L;

x = sort(randsample(1:L, ncar));%1:ncar Random number of no repetition
v = vmax * ones(1,ncar);   % start everyone initially at vmax

if animation; h = plotcirc(L,x,0.1); end

flux = 0;                  % number of cars that pass through the end
vmean = 0;
road = zeros(tmax, L);

for t = 1:tmax
    % acceleration Acceleration rule
    v = min(v+1, vmax);
    
    %collision prevention Collision avoidance
    gaps = gaplength(x,L); % determine the space vehicles have to move Vehicle distance
    v = min(v, gaps-1);
    
    % random speed drops Random deceleration
    vdrops = ( rand(1,ncar)<p );
    v = max(v-vdrops,0);
    
    % update the position
    x = x + v;
    passed = x>L;          % cars passed at time r
    x(passed) = x(passed) - L;% periodic boundary conditions Periodic boundary conditions
    
    if t>tmax/2
        flux = flux + sum(v/L); %flux = flux + sum(passed); 
        vmean = vmean + mean(v);
    end
    road(t,x) = 1;
    
    if animation; h = plotcirc(L,x,0.1,h); end
end
flux = flux/(tmax/2);
vmean = vmean/(tmax/2);

if spacetime; figure;imagesc(road);colormap([1,1,1;0,0,0]);axis image; end

% -------------------------------------------------------------------------

function gaps = gaplength(x,L)
% 
% GAPLENGTH: determine the gaps between vehicles
%
ncar = length(x);
gaps=zeros(1, ncar);
if ncar>0
    gaps = x([2:end 1]) -x;
    gaps(gaps<=0) = gaps(gaps<=0)+L;
end

% -------------------------------------------------------------------------

function h = plotcirc(L,x,dt,h)
W = 0.05;  R = 1;
ncar = length(x);

theta = [0 : 2*pi/L : 2*pi];
xc = cos(theta);     yc = sin(theta);
xinner = (R-W/2)*xc; yinner = (R-W/2)*yc;
xouter = (R+W/2)*xc; youter = (R+W/2)*yc;

xi = [xinner(x);  xinner(x+1); xouter(x+1); xouter(x)];
yi = [yinner(x);  yinner(x+1); youter(x+1); youter(x)];
if nargin == 3
    color = randperm(ncar);
    h = fill(xi,yi, color); hold on
    plot(xinner,yinner, 'k', xouter,youter, 'k','linewidth',1.5)
    plot([xinner; xouter], [yinner; youter],'k','linewidth',1.5)
    axis image; axis((R+2*W)*[-1 1 -1 1]); axis off
else
    for i=1:ncar;  set(h(i),'xdata',xi(:,i),'ydata',yi(:,i));  end
end
pause(dt)

It can be concluded that cellular automata has the following characteristics
1. Discrete space and time
2. Discrete finite state (fire, open space, growth of trees; with and without cars)
3. Cytoplasmic (no special)
4. Local action and calculation
Use: traffic problems, infectious diseases, etc
Be careful:
Cellular automata belongs to the mesh model. Pay attention to the difference of other particle models