![The notion of equations [versus constraints]](/nks/img/thumbnails/notes-5-7--the-notion-of-equations-versus-constraints--textonly.png "The notion of equations [versus constraints]")
![1D [systems based on] constraints](/nks/img/thumbnails/notes-5-7--1d-systems-based-on-constraints--textonly.png "1D [systems based on] constraints")
![[Excluded blocks in] dynamical systems theory](/nks/img/thumbnails/notes-5-7--excluded-blocks-in-dynamical-systems-theory--textonly.png "[Excluded blocks in] dynamical systems theory")
![2D [systems based on] constraints](/nks/img/thumbnails/notes-5-7--2d-systems-based-on-constraints--textonly.png "2D [systems based on] constraints")
![Numbering scheme [for 2D constraints]](/nks/img/thumbnails/notes-5-7--numbering-scheme-for-2d-constraints--textonly.png "Numbering scheme [for 2D constraints]")
![Identifying the 171 patterns [that satisfy 2D constraints]](/nks/img/thumbnails/notes-5-7--identifying-the-171-patterns-that-satisfy-2d-constraints--textonly.png "Identifying the 171 patterns [that satisfy 2D constraints]")
![Checking [tilings with] constraints](/nks/img/thumbnails/notes-5-7--checking-tilings-with-constraints--textonly.png "Checking [tilings with] constraints")
![Representing repetitive [2D] patterns](/nks/img/thumbnails/notes-5-7--representing-repetitive-2d-patterns--textonly.png "Representing repetitive [2D] patterns")
![Searching for patterns [that satisfy constraints]](/nks/img/thumbnails/notes-5-7--searching-for-patterns-that-satisfy-constraints--textonly.png "Searching for patterns [that satisfy constraints]")
![Undecidability [for 2D constraints]](/nks/img/thumbnails/notes-5-7--undecidability-for-2d-constraints--textonly.png "Undecidability [for 2D constraints]")
![NP completeness [for 2D constraints]](/nks/img/thumbnails/notes-5-7--np-completeness-for-2d-constraints--textonly.png "NP completeness [for 2D constraints]")
![Non-periodic pattern [forced by 2D constraint]](/nks/img/thumbnails/notes-5-7--non-periodic-pattern-forced-by-2d-constraint--textonly.png "Non-periodic pattern [forced by 2D constraint]")
![Other types of [2D] constraints](/nks/img/thumbnails/notes-5-7--other-types-of-2d-constraints--textonly.png "Other types of [2D] constraints")
![Forcing nested [2D] patterns](/nks/img/thumbnails/notes-5-7--forcing-nested-2d-patterns--textonly.png "Forcing nested [2D] patterns")
![Non-computable [2D] patterns](/nks/img/thumbnails/notes-5-7--non-computable-2d-patterns--textonly.png "Non-computable [2D] patterns")
![Tiling [problems]](/nks/img/thumbnails/notes-5-7--tiling-problems--textonly.png "Tiling [problems]")
![Correspondence systems [as constraints]](/nks/img/thumbnails/notes-5-7--correspondence-systems-as-constraints--textonly.png "Correspondence systems [as constraints]")
![Formal languages [and constraints]](/nks/img/thumbnails/notes-5-7--formal-languages-and-constraints--textonly.png "Formal languages [and constraints]")
The notion of equations [versus constraints]
Explanations based on constraints
1D [systems based on] constraints
[Excluded blocks in] dynamical systems theory
2D [systems based on] constraints
Numbering scheme [for 2D constraints]
Identifying the 171 patterns [that satisfy 2D constraints]
Checking [tilings with] constraints
Representing repetitive [2D] patterns
Searching for patterns [that satisfy constraints]
Undecidability [for 2D constraints]
NP completeness [for 2D constraints]
Non-periodic pattern [forced by 2D constraint]
Other types of [2D] constraints
Relation to 2D cellular automata
Relation to 1D cellular automata
Correspondence systems [as constraints]
Formal languages [and constraints]