## 62 Citations

### Hardness of Approximation for Langton's Ant on a Twisted Torus

- Computer ScienceAlgorithms
- 2020

On a twisted torus, it is demonstrated that it is PSPACE hard to determine whether the ant will ever visit almost all vertices or nearly none of them.

### A symbolic projection of Langton's Ant

- MathematicsDMCS
- 2003

The Langton's ant is studied from the point of view of topological dynamical systems and a new approach which associate a subshift to the system is proposed by establishing an algebraic characterization of the forbidden words of the subshift.

### Generalized Langton's Ant: Dynamical Behavior and Complexity

- MathematicsSTACS
- 2001

Strong spatial restrictions on the trajectory of the ant in infinite bi-regular graphs with degrees strictly greater than 4 are shown, which contrasts with the high unpredictability on the graphs of lower degrees.

### Circuit Universality of Two Dimensional Cellular Automata: A Review

- Computer Science
- 2007

A sample of models is reviewed, starting with Banks’s CA, where universality has been shown through the construction of arbitrary boolean circuits (“Circuit Universality”), in most but not all cases leading to proofs of Turing Universality.

### COMPLEXITY OF TWO DIMENSIONAL SANDPILES

- Computer Science
- 2005

It is shown that it is possible to compute logical circuits with a two-dimensional SandPile, if a neighborhood of radius two is used in Z2; crossing information becomes possible in that case, and it is concluded that for this neighborhood the Sandpile is P-complete and Turing universal.

### Time-symmetric Cellular Automata

- Computer ScienceJAC
- 2010

Time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions, is formalized in the context of cellular automata and some basic facts and relations are established.

### Langton's flies

- Mathematics
- 2008

Langton's ant is an automaton defined over a two-dimensional grid. Its movement is governed by the environment in a very simple way: it turns to the left over white vertices and to the right over…

### On the Dynamic Qualitative Behavior of Universal Computation

- Computer ScienceComplex Syst.
- 2012

The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus–as it needs to be programmed–and to its capacity for transmitting this information.

### On the Dynamic Qualitative Behaviour of Universal Computation

- Computer ScienceArXiv
- 2012

The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting information.

## References

SHOWING 1-10 OF 33 REFERENCES

### Behaviour of Multiple Generalized Langton"s Ants

- Computer Science
- 1996

This work has pursued the experimental simulation of an extension of Langton’s ant: the generalized ant, and gives a first rough classification of the patterns that arise as a consequence of their dynamical behaviour in the case of single ants.

### Rotators, periodicity, and absence of diffusion in cyclic cellular automata

- Mathematics
- 1994

Cyclic cellular automata are two-dimensional cellular automata which generalize lattice versions of the Lorentz gas and certain biochemistry models of artificial life. We show that rotators and time…

### Further Travels with My Ant

- Mathematics
- 1998

A recurring theme of this book has been computer-generated mysteries. Examples are sequences defined by simple rational recursions whose terms turn out to be integers with interesting but unexplained…

### Tracking the Automatic ANT: And Other Mathematical Explorations

- Mathematics
- 1998

Simple Sequences with Puzzling Properties Probability Paradoxes Historic Conjectures: More Sequence Mysteries Privacy Preserving Protocols Surprising Shuffles Hundreds of New Theorems in a…

### New types of diffusion in lattice gas cellular automata

- Physics
- 1993

These lectures are concerned with Lorentz lattice gas cellular automata (LLGCA), a subclass of lattice gas cellular automata (LGCA). While in LGCA identical point particles move on a lattice and upon…

### Recurrence properties of Lorentz lattice gas cellular automata

- Mathematics
- 1992

Recurrence properties of a point particle moving on a regular lattice randomly occupied with scatterers are studied for strictly deterministic, nondeterministic, and purely random scattering rules.

### Topological dynamics of flipping Lorentz lattice gas models

- Mathematics, Physics
- 1993

We study the topological dynamics of the flipping mirror model of Ruijgrok and Cohen with one or an infinite number of particles. In particular we prove the topological transitivity and topological…

### Diffusion and propagation in triangular Lorentz lattice gas cellular automata

- Mathematics, Physics
- 1991

The diffusion process of point particles moving on regular triangular and random lattices, randomly occupied with stationary scatterers (a Lorentz lattice gas cellular automaton), is studied, for…

### Propagation and Organization in Lattice Random Media

- Physics, Mathematics
- 1999

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a…