1.要求

小球在如下图5个点间移动，其下一个位置有一下几种情况：

如果当前在最左侧位置，即x=1，则下一次到x=2位置处；
如果当前在最右侧位置，即x=5，则下一次到x=4位置处；
如果当前在x=2/x=3/x=4位置，则下一次各有三分之一的概率向左移动一格、向右移动一格、保持不动。

2.matlab代码

clear;
close all;
clc;
speed = 4; %速度
marksize = 30;
speed_fan = 1/speed;%取反
x=1:0.01:5;%x轴
y=ones(size(x));%y轴
pos = [1, 2, 3, 4, 5];%五个位置
next = randi(length(pos));%初始位置
fig = figure('CloseRequestFcn',@my_closereq);%图窗
plot(x,y, 'b-', 'linewidth', 2);%线
hold on;
axis equal;
axis off;
for t=1:length(pos)
    plot([pos(t), pos(t)],[1, 1.1],'b', 'linewidth', 2);%点
    text(t-0.03, 0.9, num2str(t));
    hold on;
end
global flag
flag = 1;%标记是否关闭
while flag
    pre = next;
    if or(or(next==2, next==3), next==4)%2，3，4位置
        t = randi(3);
        if t==1%左移
            next = next -1;
        elseif t==3%右移
            next = next + 1;
        end
    elseif next==1%右移
        next = 2;
    else%左移
        next = 4;
    end
    for move=linspace(pre, next,100)%游动
        h = plot(move,1,'r.', 'markersize',marksize);
        pause(speed_fan*0.01);%游动暂停
        set(h,'Visible','off');
        delete(h);
    end
    h = plot(next,1,'r.', 'markersize',marksize);%最后位置
    hold on;
    % pause(speed_fan*1);%暂停
    if flag==1
        set(h,'Visible','off');%删除
        delete(h);
    end
end

function my_closereq(~,~)%关闭图窗按钮
global flag
    delete(gcf)
    flag = 0;%关闭标志
    return 
end

实现效果：

演示视频：

链接：马尔可夫过程-粒子游动演示视频

3.升级

实时显示到达边界的次数，两个边界各分别显示；
到达最右侧边界后，下一次跳到随机位置。

4.matlab实现

clear;
close all;
clc;
speed = 4; %速度
marksize = 30;
speed_fan = 1/speed;%取反
x=1:0.01:5;%x轴
y=ones(size(x));%y轴
pos = [1, 2, 3, 4, 5];%五个位置
num = zeros(1,2);
sum_num1 = 0;
sum_num = 0;
next = randi(length(pos));%初始位置
fig = figure('CloseRequestFcn',@my_closereq);%图窗
plot(x,y, 'b-', 'linewidth', 2);%线
hold on;
axis equal;
axis off;
for t=1:length(pos)
    plot([pos(t), pos(t)],[1, 1.1],'b', 'linewidth', 2);%点
    text(t-0.03, 0.9, num2str(t));
    hold on;
end
 h = plot(next,1,'r.', 'markersize',marksize);
 text_num = text(5-0.03, 1.3, num2str(sum_num));
 text_num1 = text(1-0.03, 1.3, num2str(sum_num1));
 hold on;
global flag
flag = 1;%标记是否关闭
while flag
    if sum(num)==2
        num = zeros(1, 2);
        next = randi(length(3)) + 1;
        continue;
    end
    pre = next;
    delete(text_num);
    delete(text_num1);
    text_num = text(5-0.03, 1.3, num2str(sum_num));
    text_num1 = text(1-0.03, 1.3, num2str(sum_num1));
    if or(or(next==2, next==3), next==4)%2，3，4位置
        t = randi(3);
        if t==1%左移
            next = next -1;
        elseif t==3%右移
            next = next + 1;
        end
    elseif next==1%右移
        next = 2;
    else%左移
        next = 4;
        continue;
    end
    for move=linspace(pre, next,100)%游动
        set(h, 'xdata', move);
        pause(speed_fan*0.01);%游动暂停
    end
    set(h, 'xdata', next);
    if next==1
        num(next) = 1;
        sum_num1 = sum_num1 + 1;
    elseif next==5
        num(2) = 1;
        sum_num = sum_num + 1;
    end
    hold on;
end

function my_closereq(~,~)%关闭图窗按钮
global flag
    delete(gcf)
    flag = 0;%关闭标志
    out = 1
    return 
end