A 简介
1 历史
最初的元胞自动机是由冯 · 诺依曼在 1950 年代为模拟生物 细胞的自我复制而提出的. 但是并未受到学术界重视.
1970 年, 剑桥大学的约翰 · 何顿 · 康威设计了一个电脑游戏 “生命游戏” 后, 元胞自动机才吸引了科学家们的注意.
1983 年 S.Wolfram 发表了一系列论文. 对初等元胞机 256 种 规则所产生的模型进行了深入研究, 并用熵来描述其演化行 为, 将细胞自动机分为平稳型, 周期型, 混沌型和复杂型.
2 应用
- 社会学: 元胞自动机经常用于研究个人行为的社会性, 流行 现象. 例如人口迁移, 公共场所内人员的疏散, 流行病传播.
- 图形学: 元胞自动机以其特有的结构的简单性, 内在的并行 性以及复杂计算的能力成为密码学中研究的热点方向之一
- 物理学: 在物理学中, 元胞自动机已成功的应用于流体, 磁 场, 电场, 热传导等的模拟. 例如格子气自动机.
3 一维元胞自动机——交通规则
定义:
-
元胞分布于一维线性网格上.
-
元胞仅具有车和空两种状态.
-
元胞状态由周围两邻居决定.
规则:研究的变化对象只是中间的格子,后面的车子要比前面的车子起步延迟1格。
4 二维元胞自动机——生命游戏
定义:
-
元胞分布于二维方型网格上.
-
元胞仅具有生和死两种状态.
-
元胞状态由周围八邻居决定.
规则:
骷髅:死亡;笑脸:生存
周围有三个笑脸,则中间变为笑脸
少于两个笑脸或者多于三个,中间则变死亡。
5 什么是元胞自动机
离散的系统: 元胞是定义在有限的时间和空间上的, 并且元 胞的状态是有限.
动力学系统: 元胞自动机的举止行为具有动力学特征.
简单与复杂: 元胞自动机用简单规则控制相互作用的元胞 模拟复杂世界.
6 构成要素
(1)元胞 (Cell)
元胞是元胞自动机基本单元:
- 状态: 每一个元胞都有记忆贮存状态的功能.
- 离散: 简单情况下, 元胞只有两种可能状态; 较复杂情况下, 元胞具有多种状态.
- 更新: 元胞的状态都安照动力规则不断更新.
(2)网格 (Lattice)
不同维网格
常用二维网格
(3)邻居 (Neighborhood)
(4)边界 (Boundary)
反射型:以自己作为边界的状态
吸收型:不管边界(车开到边界就消失)
(5)规则(状态转移函数)
定义:根据元胞当前状态及其邻居状况
确定下一时刻该元胞状态的动力学函数, 简单讲, 就是一个状态转移函数.
分类 :
- 总和型: 某元胞下时刻的状态取决于且仅取决于它所有邻居 的当前状态以及自身的当前状态.
- 合法型: 总和型规则属于合法型规则. 但如果把元胞自动机 的规则限制为总和型, 会使元胞自动机具有局限性.
(6)森林火灾
绿色:树木;红色:火;黑色:空地。
三种状态循环转化:
树:周围有火或者被闪电击中就变成火。
空地:以概率p变为树木
理性分析:红为火;灰为空地;绿是树
元胞三种状态的密度和为1
火转化为空地的密度等于空地转换为树的密度(新长出来的树等于烧没的树)
f ff是闪电的概率:远远小于树生成的概率;T s m a x T_{smax}Tsmax是一大群树被火烧的时间尺度
程序实现
周期性边界条件
购进啊
其中的数字为编号
构建邻居矩阵
上面矩阵中的数字编号,对应原矩阵相同位置编号的上邻居编号,一 一对应
同样道理:
(7)交通概念
车距和密度
流量方程
守恒方程
时空轨迹(横轴是空间纵轴为时间)
红线横线与蓝色交点表示每个时间车的位置。
如果是竖线则表示车子在该位置对应的时间
宏观连续模型:
最常用的规则:
红色条表示速度是满的。
1 加速规则:不能超过v m a x ( 2 格 / s ) v_{max}(2格/s)vmax(2格/s)
2 防止碰撞:不能超过车距
理论分析:
结果分析: 密度与流量
第一个图:横坐标是归一化后的密度,纵坐标是车流量。第二个图:理论值与CA的结果
结果分析: 时空轨迹
中间的深色区域是交通堵塞的区域。
function varargout = renyuanshusan(varargin)
% RENYUANSHUSAN M-file for renyuanshusan.fig
% RENYUANSHUSAN, by itself, creates a new RENYUANSHUSAN or raises the existing
% singleton*.
%
% H = RENYUANSHUSAN returns the handle to a new RENYUANSHUSAN or the handle to
% the existing singleton*.
%
% RENYUANSHUSAN('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in RENYUANSHUSAN.M with the given input arguments.
%
% RENYUANSHUSAN('Property','Value',...) creates a new RENYUANSHUSAN or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before renyuanshusan_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to renyuanshusan_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help renyuanshusan
% Last Modified by GUIDE v2.5 08-Mar-2014 16:52:27
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @renyuanshusan_OpeningFcn, ...
'gui_OutputFcn', @renyuanshusan_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before renyuanshusan is made visible.
function renyuanshusan_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to renyuanshusan (see VARARGIN)
% Choose default command line output for renyuanshusan
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes renyuanshusan wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = renyuanshusan_OutputFcn(~, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
function edit1_Callback(~, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit1 as text
% str2double(get(hObject,'String')) returns contents of edit1 as a double
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit2_Callback(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit2 as text
% str2double(get(hObject,'String')) returns contents of edit2 as a double
% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit3_Callback(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit3 as text
% str2double(get(hObject,'String')) returns contents of edit3 as a double
% --- Executes during object creation, after setting all properties.
function edit3_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit4_Callback(hObject, eventdata, handles)
% hObject handle to edit4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit4 as text
% str2double(get(hObject,'String')) returns contents of edit4 as a double
% --- Executes during object creation, after setting all properties.
function edit4_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit5_Callback(hObject, eventdata, handles)
% hObject handle to edit5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit5 as text
% str2double(get(hObject,'String')) returns contents of edit5 as a double
% --- Executes during object creation, after setting all properties.
function edit5_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit6_Callback(hObject, eventdata, handles)
% hObject handle to edit6 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit6 as text
% str2double(get(hObject,'String')) returns contents of edit6 as a double
% --- Executes during object creation, after setting all properties.
function edit6_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit6 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on slider movement.
function slider1_Callback(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
x=get(hObject,'value');
set(handles.text16,'string',num2str(x));
% --- Executes during object creation, after setting all properties.
function slider1_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
function edit8_Callback(hObject, eventdata, handles)
% hObject handle to edit8 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit8 as text
% str2double(get(hObject,'String')) returns contents of edit8 as a double
% --- Executes during object creation, after setting all properties.
function edit8_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit8 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on slider movement.
function slider2_Callback(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
x=get(hObject,'value');
set(handles.text18,'string',num2str(x));
% --- Executes during object creation, after setting all properties.
function slider2_CreateFcn(hObject, eventdata, handles)
% hObject handle to slider2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
function edit9_Callback(hObject, eventdata, handles)
% hObject handle to edit9 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit9 as text
% str2double(get(hObject,'String')) returns contents of edit9 as a double
% --- Executes during object creation, after setting all properties.
function edit9_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit9 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% if Pop_beikun> Pop_beikun1;
% Pop_beikun1=Pop_beikun;
set(handles.text27,'string',num2str(Pop_beikun));
% end
if Pop==Pop_beikun||sum(sum(Dst_S))==col*row;
set(handles.text27,'string',num2str(Pop));
break
end
end
hold off
set(handles.text33,'string','仿真结束!!');
return
%%%%%%%%%%%%%%%%%%%%%%
% --- Executes on button press in pushbutton3.
function Exit_S=pushbutton3_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
function edit11_Callback(hObject, eventdata, handles)
% hObject handle to edit11 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit11 as text
% str2double(get(hObject,'String')) returns contents of edit11 as a double
% --- Executes during object creation, after setting all properties.
function edit11_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit11 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles,Exit_S)
% hObject handle to pushbutton4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
close
% --- Executes on button press in pushbutton5.
function pushbutton5_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
pause off
完整代码或者代写添加QQ1575304183