基于MATLAB的元胞自动机掉落模拟器

本文介绍了一种基于MATLAB的元胞自动机（Cellular Automata）掉落模拟器。该模拟器通过固定概率使元胞向其四个相邻位置扩散。

以下是实现该模拟器的MATLAB代码示例：

function ClumsyChild(c1, m)
% 实现元胞以固定的概率向相邻的4个元胞扩散
% Example:
% ClumsyChild(0.1, 0.1);
% Author's email: zjliu2001@163.com
N = 100;
rand('state', 0);
A = randperm(N^2);
S = zeros(N);
S(A(1:3000)) = 3; % 30%的位置是状态3
S(A(3001:5000)) = 1; % 20%的位置是状态1
S(A(5001:6000)) = 2; % 10%的位置是状态2
clear A;
close all;
figure('position', [159 42 567 427]);
imagesc([1:4]');
set(gca, 'YAxisLocation', 'right');
set(gca, 'position', [0.84, 0.12, 0.1, 0.8]);
set(gca, 'xtick', []);
set(gca, 'ytick', [1:4]);
set(gca, 'yticklabel', num2str([0:3]'));
axes('position', [0.06, 0.12, 0.7, 0.8]);
H = imagesc(S);
set(gcf, 'position', [159 42 485 427]);
set(gcf, 'doublebuffer', 'on');
xlabel('请按空格键停止程序！', 'fontsize', 12, 'color', 'r');
title(['c1=' num2str(c1) ' m=' num2str(m)]);
k = 1;
while k
    pause(0.5);
    s = get(gcf, 'currentkey');
    if strcmp(s, 'space')
        clc;
        k = 0;
    end
    S = evolvement(S, c1, m);
    set(H, 'CData', S);
end
figure(gcf);

function S = evolvement(S, c1, m)
    P = zeros(size(S));
    Da = rand(size(S));
    Da(Da > 1 - c1) = 1;
    Da(Da <1 - c1) = 0;
    P(S == 1 | S == 2) = 1;
    R = round(rand(size(S)) + 1);
    P = P .* R .* Da;
    V = round(rand(size(S)) * 3) + 1;
    V = V .* P; % V是速度方向:
    % 1 --- up
    % 2 --- down
    % 3 --- left
    % 4 --- right
    V(1, V(1, :) == 1) = 0;
    V(end, V(end, :) == 2) = 0;
    V(V(:, 1) == 3, 1) = 0;
    V(V(:, end) == 4, end) = 0;
    % 产生后代
    [x, y] = find(V == 1);
    DD = zeros(size(S));
    DD(x - 1, y) = P(x - 1, y);
    S(S == 0 | S == 2 & DD == 1) = 1;
    S(S == 0 & DD == 2) = 2;
    [x, y] = find(V == 2);
    DD = zeros(size(S));
    DD(x + 1, y) = P(x + 1, y);
    S(S == 0 | S == 2 & DD == 1) = 1;
    S(S == 0 & DD == 2) = 2;
    [x, y] = find(V == 3);
    DD = zeros(size(S));
    DD(x, y - 1) = P(x, y - 1);
    S(S == 0 | S == 2 & DD == 1) = 1;
    S(S == 0 & DD == 2) = 2;
    [x, y] = find(V == 4);
    DD = zeros(size(S));
    DD(x, y + 1) = P(x, y + 1);
    S(S == 0 | S == 2 & DD == 1) = 1;
    S(S == 0 & DD == 2) = 2;
    Dr = rand(size(S));
    S(S <3 & Dr 

该代码首先初始化一个100x100的网格，其中30%的位置是状态3，20%的位置是状态1，10%的位置是状态2。然后，通过固定概率使元胞向其四个相邻位置扩散，并在每个时间步中更新网格状态。用户可以通过按空格键停止程序。