All Questions
Tagged with symbolic-dynamics cellular-automata
8 questions
1
vote
1
answer
155
views
Properties of limit set for cellular automata
Is anyone familiar with results about properties of the limit set of the local rule for a cellular automaton? I haven't been able to find any good materials on the subject from an initial search, and ...
- 633
2
votes
1
answer
183
views
A sensitive 2-dimensional cellular automaton with a blocking word
I'am a Ph.D student in the domain of discrete dynamical systems. My thesis is about spectral properties of cellular automata in higher dimension.
Kurka gives a classification for one dimensional ...
- 171
0
votes
0
answers
120
views
Growing gliders under rule 110
I found a glider in the evolution space of rule 110 that grows constantly in size. Normal gliders live in the so-called ether, e.g. the so-called E-glider:
Other – often complex – gliders exist in an ...
- 9,730
0
votes
0
answers
88
views
Relation between symbolic substitution and cellular automata
I recently asked this on Math Stackexchange recently in this thread. I was told that there is a relation between symbolic substitutions and cellular automata. I'm vaguely familiar with Cobham's ...
- 63.9k
1
vote
1
answer
139
views
A special kind of pseudo-garden eden states in cellular automata
I'm currently investigating Wolfram's elementary cellular automata on finite grids with periodic boundary conditions, i.e. on $\mathbb{Z}/k$ for different $k$.
It is clear that for each rule $R$ and ...
- 63.9k
8
votes
1
answer
436
views
The graph of Rule 110 and vertices degree
Consider the elementary cellular automaton called Rule 110 (famous for being Turing complete):
It induces a map $R: \mathbb{N} \to \mathbb{N}$ such that the binary representation of $R(n)$ is ...
- 6,652
3
votes
2
answers
368
views
Periodic configurations for elementary cellular automata
Let $L$ be an elementary cellular automaton. Then $L$ acts on $\{0,1\}^{\mathbb{Z}}$. We say that a configuration $w\in\{0,1\}^{\mathbb{Z}}$ is periodic if $L^{(n)}(w)=w$ for some $n\in\mathbb{N}$.
...
- 6,652
3
votes
2
answers
398
views
Does the 2-shift map have a root automorphism?
By the 2-shift map I mean the map $T:\{0,1\}^\mathbb{Z}\to \{0,1\}^\mathbb{Z}$ that shifts the sequence leftwise. By a root I mean an homeomorphism $\psi:\{0,1\}^\mathbb{Z}\to\{0,1\}^\mathbb{Z}$ that ...
- 63.9k