Hydra game - Wikipedia
In mathematics, specifically in graph theory and number theory, a hydra game is a single-player iterative mathematical game played on a mathematical tree called a hydra where, usually, the goal is to cut off the hydra's "heads" while the hydra simultaneously expands itself.
Buchholz hydra - Wikipedia
In mathematics, especially mathematical logic, graph theory and number theory, the Buchholz hydra game is a type of hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree.
Mathematics and Computation | The hydra game - Andrej
2008年2月2日 · A hydra is a finite tree, with a root at the bottom. The object of the game is to cut down the hydra to its root. At each step, you can cut off one of the heads, after which the hydra grows new heads according to the following rules:
Hydra game: An example of a counterintuitive mathematical result.
2014年6月4日 · The Hydra game! Imagine that you are Hercules, and you were given the task to slay the Hydra. Here is one possible hydra:
The Mathematical Hydra - Math Mondays
2019年9月29日 · We assign an ordinal number to each hydra, in such a way that cutting off a head produces a hydra with a strictly smaller ordinal. As we play the hydra game, the sequence of hydras we encounter produces a corresponding sequence of ordinals.
Kirby-Paris hydra | Googology Wiki | Fandom
The Kirby-Paris hydra game is a one-player game played on a tree that can last a very large number of turns. It gives rise to a function \(\text{Hydra}(n)\) that eventually dominates all recursive functions which are provably total in Peano arithmetic , and is itself provably total in PA + "\(\varepsilon_0\) is well-ordered", and the game is ...
The Hydra Game algorithm - Computer Science Stack Exchange
2024年4月18日 · You start with the Hydra being a straight line of vertices and edges, with a single root and a single leaf. At each step, call it k k, you always pick the right-most leaf/head and chop it off, whereafter k k leaves will regrow from the grandfather …
Amiko hydras - Komi Amiko
2020年6月7日 · Hydras are a classic iterative game played on trees, known by googologists for the fast-growing functions derived from them and by serious mathematicians for their contributions to ordinal analysis.
graph theory - Is it really impossible to lose the Hydra game ...
2016年5月22日 · Here are the rules of the game, as I understand them. A hydra is a rooted tree. Its leaves are called "heads". The player (Hercules) must kill the hydra (i.e. reduce it to only its root node) by chopping off its heads. To chop of a head, we first remove it from the tree. If this creates a new leaf node, it becomes a new head.
The Hydra Game – Numberphile – TOM ROCKS MATHS
2024年4月19日 · The Hydra Game – Numberphile Tom talks Hercules and the Hydra Game. A single branch length 5, each time you chop off the right-most head, n grow back from the grand-parent (where n is the step number you are currently at).
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