论文
arXiv
CellularAutomata
中文标题
基于碰撞的逻辑在 Lenia 中的实现及其组合边界
English Title
Collision-based logic in Lenia and its composition boundary
Chakshu Gupta
发布时间
2026/9/1 22:56:13
来源类型
preprint
语言
en
摘要
中文对照

诸如 Lenia 这类连续细胞自动机(continuous cellular automata)可自发产生类生命、自推进的图案,其中包括 Orbium 滑翔机(Orbium glider):它沿直线运动,并以固定的呼吸周期脉动。基于碰撞的逻辑——即通过运动图案之间的碰撞实现计算——已在离散细胞自动机及连续物理介质中确立。而在连续细胞自动机中,计算迄今均需通过对规则进行训练而嵌入,尚不清楚固定规则的自动机(如 Lenia)能否支持通用的基于碰撞的计算。本文基于 Orbium 滑翔机的碰撞构造出一个 INHIBIT 门。在四种连续细胞自动机规则类型所搜索的所有图案中,Orbium 滑翔机是唯一被证实能在与自身副本碰撞后仍完整存留的图案。该门中,一个控制滑翔机将信号滑翔机偏转出其输出路径,因此仅当无控制信号存在时,输出路径才携带信号。该门在呼吸周期全部二十四个相位及控制信号的九个整数偏移量下均能可靠阻断。两个此类门串联构成一个 AND-NOT 链,对全部八种输入组合均正确工作。相比之下,将信号路由至该单一链之外尚未得到验证:偏转后的信号无法恢复至固定着陆位置,且未发现可复用的滑翔机吸收器。因此,Lenia 中基于碰撞计算的当前核心开放问题,已从‘是否存在逻辑门’进一步收窄为‘偏转后的信号能否被准确送达下游逻辑门’——这是将逻辑门扩展至单一直线链之外所必需的下一步。

English Original

Continuous cellular automata such as Lenia spontaneously produce lifelike, self-propelling patterns, including the Orbium glider, which travels in a straight line while pulsing through a fixed breathing cycle. Collision-based logic, where moving patterns compute by colliding, is established in discrete cellular automata and continuous physical media. Within continuous cellular automata, computation has so far been trained into the rule rather than emerging from collisions, and whether a fixed-rule automaton like Lenia can support general collision-based computation remains open. This paper constructs an INHIBIT gate from collisions of the Orbium glider. Of the patterns searched across four continuous-CA rule types, the Orbium glider is the only one shown to survive a collision with both copies intact. A control glider deflects a signal glider off its output line, so the output carries a signal only when no control is present. The gate blocks across all twenty-four phases of the breathing cycle and nine integer offsets of the control. Two such gates in series, with one signal line and two controls, compose into an AND-NOT chain, correct on all eight input combinations. By contrast, routing a signal beyond that single chain is undemonstrated. A deflected signal is not restored to a fixed landing position, and no reusable absorber for the surviving gliders was found. The immediate open question for collision-based computation in Lenia therefore narrows from whether a gate exists to whether a deflected signal can be delivered to a downstream gate, the next requirement for composing the gate beyond a single straight chain.

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元数据
arXiv2609.01348v1
来源arXiv
类型论文
抽取状态raw
关键词
CellularAutomata
cs.ET
nlin.CG
nlin.PS