代换系统
SubstitutionSystem 生成表示给定初始状态和按照基本规则迭代应用的演变的列表.
以下为初始状态和基本规则.
In[1]:=
![Click for copyable input](assets.zh/substitution-systems/In_54.png)
init = "\[Wolf]";
rules = {"\[HappySmiley]" -> "\[Wolf]\[HappySmiley]",
"\[Wolf]" -> "\[HappySmiley]"};
用 SubstitutionSystem 获取 8 个迭代后的演变.
In[2]:=
![Click for copyable input](assets.zh/substitution-systems/In_55.png)
SubstitutionSystem[{"\[HappySmiley]" -> "\[Wolf]\[HappySmiley]",
"\[Wolf]" -> "\[HappySmiley]"}, "\[Wolf]", 8] // Column
Out[2]=
![](assets.zh/substitution-systems/O_60.png)
用二维基本规则构建谢尔宾斯基地毯(Sierpiński carpet).
In[3]:=
![Click for copyable input](assets.zh/substitution-systems/In_56.png)
rules2D = {1 -> {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}},
0 -> ConstantArray[0, {3, 3}]};
用 RulePlot 可视化该代换系统.
In[4]:=
![Click for copyable input](assets.zh/substitution-systems/In_57.png)
RulePlot@SubstitutionSystem[rules2D]
Out[4]=
![](assets.zh/substitution-systems/O_61.png)
生成谢尔宾斯基地毯.
In[5]:=
![Click for copyable input](assets.zh/substitution-systems/In_58.png)
ArrayPlot /@ SubstitutionSystem[rules2D, {{1}}, 5]
Out[5]=
![](assets.zh/substitution-systems/O_62.png)