Confusion in the Garden of Eden

Abduction, unpredictability and Garden of Eden

Exact Enumeration of Garden of Eden Partitions

We give two proofs for a formula that counts the number of partitions of n that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in Section 1. Section 2 presents a generating function argument for the formula based on Dyson’s original paper where the rank of a partition is defined. Section 3 gi...

The Garden-of-eden Theorem for Finite Configurations

In [l] Moore showed that the existence of mutually erasable configurations in a two-dimensional tessellation space is sufficient for the existence of Garden-of-Eden configurations. In [2 ] Myhill showed that the existence of mutually indistinguishable configurations is both necessary and sufficient for the existence of Garden-of-Eden configurations. After redefining the basic concepts with some...

Some Extensions of the Moore-Myhill Garden of Eden Theorem

The Garden of Eden theorem: old and new

We review topics in the theory of cellular automata and dynamical systems that are related to the Moore-Myhill Garden of Eden theorem.