• Corpus ID: 34157943

Definition and Behavior of Langton's Ant in Three Dimensions

@article{Hamann2003DefinitionAB,
  title={Definition and Behavior of Langton's Ant in Three Dimensions},
  author={Heiko Hamann},
  journal={Complex Syst.},
  year={2003},
  volume={14}
}
The “virtual ant” automaton was invented by C. Langton [1]. It has an interesting behavior that has been studied in several researches. A definition of generalized ants in three dimensions, as an extension to Langton’s ant, is given here. The phenomenon of periodic motion with drift, the so-called “highway,” is also observed in three dimensions but occurs in very different forms. Two classification systems of three-dimensional ants according to the period length of their highways and the… 
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References

SHOWING 1-7 OF 7 REFERENCES
Behaviour of Multiple Generalized Langton"s Ants
TLDR
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.
MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES
We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called
Rotators, periodicity, and absence of diffusion in cyclic cellular automata
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
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
Studying artificial life with cellular automata
Complex systems
  • B. Keepence, M. Mannion
  • Computer Science
    Proceedings International Conference and Workshop on Engineering of Computer-Based Systems
  • 1997
TLDR
A fresh look is presented at the nature of complexity in the building of computer based systems with a wide range of reasons all the way from hardware failures through software errors right to major system level mistakes.
Further Ant-ics
  • Mathematical Intelligencer
  • 1994