# Odd-Rule Cellular Automata on the Square Grid

@article{Ekhad2015OddRuleCA, title={Odd-Rule Cellular Automata on the Square Grid}, author={Shalosh B. Ekhad and N. J. A. Sloane and Doron Zeilberger}, journal={arXiv: Combinatorics}, year={2015} }

An \odd-rule" cellular automaton (CA) is dened by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF. We classify all the odd-rule CAs dened

## 2 Citations

### On the Number of ON Cells in Cellular Automata

- Computer Science
- 2015

If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain \odd-rule" CAs, including Rule 150, Rule 614, and Fredkin’s Replicator, the…

### A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata

- Computer Science
- 2015

A meta-algorithm is developed that produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears as a coefficient when the polynomial is raised to the power n and the coefficients are readmodulo p.

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If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain \odd-rule" CAs, including Rule 150, Rule 614, and Fredkin’s Replicator, the…

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A meta-algorithm is developed that produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears as a coefficient when the polynomial is raised to the power n and the coefficients are readmodulo p.

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