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本文提出利用“锯齿度”（jaggedness）指标刻画 Life-Like 网络自动机规则空间的结构，并将其作为混沌性与敏感性的理论代理，引导启发式规则选择策略。实验表明该方法在分类精度上接近全局最优（差距在 5% 以内），同时相比穷举搜索降低约 90% 的计算开销。
本文提出"空间感应头"（spatial induction heads），一种两层 gather-and-match 电路，解释 Transformer 如何在多维细胞自动机的序列化数据中进行上下文学习。研究表明，该电路可逼近贝叶斯后验并在确定性规则上实现精确预测，训练后的两层 Transformer 能泛化到未见过的规则。
This paper compares LSTM Universal Transformer (LSTM-UT) with other recurrent-depth transformers on cellular automata tasks, demonstrating that LSTM-UT improves depth extrapolation and delayed recall through bounded gated memory.
This paper presents CARL, an autotelic reinforcement learning framework that autonomously discovers and controls self-organizing phenomena in complex systems like Lenia cellular automata, demonstrating capabilities in steering solitons and zero-shot generalization.
A critical review of Stephen Wolfram's book 'A New Kind of Science', questioning his egomania and scientific claims regarding cellular automata.
The article describes GenOS, a custom multi-agent framework that autonomously evolved Rust algorithms to solve the NP-Hard Reverse Game of Life problem, discovering three optimization paradigms and proving a mathematical limit of 378/400.
The author shares his reflections on Stephen Wolfram's A New Kind of Science, arguing that continuous calculus is only an engineering compromise made for a discrete universe in an era of scarce computing power, and discusses how computational irreducibility challenges the traditional paradigm of prediction.
Heikki Lotvonen built a radically simple co-op drawing app for toddlers called Mr. Baby Paint, accidentally discovering a flood-fill cellular automaton and developing pixel-fattening algorithms for bitmap fonts.
Grid Programs proposes a two-dimensional grid programming model where instructions are placed on a grid, and a pointer controls the flow by moving up, down, left, and right, without the need for variable names. It has been proven Turing complete, opening up new design spaces for visual programming, cellular automaton hardware, and code obfuscation.
The article describes building GOLDE, a simulator for Conway's Game of Life using the HashLife algorithm in modern C++, capable of simulating trillions of generations instantly.
CAX is a high-performance open-source library for cellular automata research, built on JAX. It accelerates simulations up to 2000x and supports discrete and continuous automata in arbitrary dimensions.