Garden of Eden (mathematics) (nonfiction): Difference between revisions
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In a [[Cellular | In a [[Cellular automaton (nonfiction)|cellular automaton]], a '''Garden of Eden''' is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot appear later in the evolution of the automaton. | ||
John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere. | [[John Tukey (nonfiction)|John Tukey]] named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere. | ||
A Garden of Eden is determined by the state of every cell in the automaton (usually a one- or two-dimensional infinite square lattice of cells). However, for any Garden of Eden there is a finite pattern (a subset of cells and their states, called an orphan) with the same property of having no predecessor, no matter how the remaining cells are filled in. A configuration of the whole automaton is a Garden of Eden if and only if it contains an orphan. For one-dimensional cellular automata, orphans and Gardens of Eden can be found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless, computer searches have succeeded in finding these patterns in Conway's Game of Life. | A Garden of Eden is determined by the state of every cell in the automaton (usually a one- or two-dimensional infinite square lattice of cells). However, for any Garden of Eden there is a finite pattern (a subset of cells and their states, called an orphan) with the same property of having no predecessor, no matter how the remaining cells are filled in. A configuration of the whole automaton is a Garden of Eden if and only if it contains an orphan. For one-dimensional cellular automata, orphans and Gardens of Eden can be found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless, computer searches have succeeded in finding these patterns in Conway's Game of Life. | ||
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== Fiction cross-reference == | == Fiction cross-reference == | ||
* [[John Tukey (nonfiction)]] | |||
== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
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[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Cellular automata (nonfiction)]] | |||
[[Category:Mathematics (nonfiction)]] | [[Category:Mathematics (nonfiction)]] | ||
Latest revision as of 11:49, 18 June 2017
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot appear later in the evolution of the automaton.
John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere.
A Garden of Eden is determined by the state of every cell in the automaton (usually a one- or two-dimensional infinite square lattice of cells). However, for any Garden of Eden there is a finite pattern (a subset of cells and their states, called an orphan) with the same property of having no predecessor, no matter how the remaining cells are filled in. A configuration of the whole automaton is a Garden of Eden if and only if it contains an orphan. For one-dimensional cellular automata, orphans and Gardens of Eden can be found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless, computer searches have succeeded in finding these patterns in Conway's Game of Life.
The Garden of Eden theorem of Moore and Myhill asserts that a cellular automaton on the square grid, or on a tiling of any higher dimensional Euclidean space, has a Garden of Eden if and only if it has twins, two finite patterns that have the same successors whenever one is substituted for the other.
Fiction cross-reference
Nonfiction cross-reference
External links:
- Garden of Eden (cellular automaton) @ Wikipedia