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Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata.
Bilal Khan1, Yuri Cantor2, Kirk Dombrowski1
1Department of Sociology, University of Nebraska-Lincoln, Lincoln, Nebraska, USA.
Journal of Computer Science and Systems Biology
|September 24, 2016
Summary
Boolean organisms with a cell count that is a power of 2 inevitably evolve to a state of all zeros. This lack of dynamics suggests evolutionary disadvantage, highlighting the importance of cell diversity for adaptability.
Area of Science:
- Theoretical computer science
- Evolutionary computation
- Cellular automata
Background:
- Synchronous Boolean organisms model systems with discrete states and local interactions.
- Cellular dynamics are influenced by neighboring cell values, leading to emergent patterns.
Purpose of the Study:
- To investigate the relationship between cell count, dynamics, and evolutionary adaptiveness in Boolean organisms.
- To identify conditions under which these organisms exhibit structural dynamics or lack thereof.
Main Methods:
- Mathematical analysis of synchronous Boolean cellular automata.
- Proof of necessary and sufficient conditions for convergence to a homogeneous state.
- Computational experiments to explore growth dynamics and homogeneity assumptions.
Main Results:
- Organisms with a cell count that is a power of 2 necessarily converge to a state where all cells are 0.
- Conversely, if an organism's cell count is a power of 2, it will always converge to the all-0 state.
- Lack of structural dynamics in the all-0 state implies reduced adaptiveness.
Conclusions:
- A cell count that is a power of 2 is evolutionarily disadvantageous due to a lack of adaptive dynamics.
- Organisms must depart from cellular homogeneity to achieve growth beyond a power of 2 while maintaining adaptive dynamics.
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