A class of cellular automata modeling winnerless competition

Area of Science:

• Computational neuroscience
• Theoretical computer science
• Dynamical systems

Background:

• Neural units provide a model for sensory coding.
• Cellular automata (CA) offer a framework for spatio-temporal information processing.
• Dynamically competitive networks inspire new computational models.

Purpose of the Study:

• To explore the feasibility of spatio-temporal encoding in cellular automata (CA).
• To estimate the information capacity of CA by analyzing their attractor sets.
• To investigate the properties of attractors in two-dimensional CA.

Main Methods:

• Utilizing neural unit concepts to define CA models.
• Estimating spatio-temporal information capacity via the information capacity of the attractor set.
• Detailed analysis of two-dimensional CA.

Main Results:

• Demonstrated the feasibility of spatio-temporal encoding in a class of CA.
• Established that the information capacity is linked to the finitely specified attractor set.
• Presented a two-dimensional CA example where the attractor is not a subshift.

Conclusions:

• Cellular automata can be designed for effective spatio-temporal encoding.
• The attractor set's information capacity is a key metric for evaluating CA performance.
• The study expands understanding of CA dynamics beyond traditional subshift definitions.