We describe a method which exploits discrete dynamical systems to generate suitable classes of polyominoes. We apply the method to design an algorithm that uses O(n) space to generate in constant amortized time all polyominoes corresponding to hole-free partially directed animals consisting of n sites on the square grid. By implementing the algorithm in C++ we have obtained a new sequence that does not appear in the On-Line Encyclopedia of Integer Sequences.
A dynamical system approach to polyominoes generation
massazza
2021-01-01
Abstract
We describe a method which exploits discrete dynamical systems to generate suitable classes of polyominoes. We apply the method to design an algorithm that uses O(n) space to generate in constant amortized time all polyominoes corresponding to hole-free partially directed animals consisting of n sites on the square grid. By implementing the algorithm in C++ we have obtained a new sequence that does not appear in the On-Line Encyclopedia of Integer Sequences.
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