Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife

Rafler, Stephan

doi:10.48550/arxiv.1111.1567

Cited by 3 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Rafler [Raf11] argues that one of the defining features of GoL is the glider [Gar70], a creature that moves smoothly across the grid and wraps around at the edges. Rafler describes a continuous version of GoL featuring a glider.…”

Section: Smoothlifementioning

confidence: 99%

“…This gives an inner disk of width r i (representing the cell x) and an outer ring of width |ro-r i | (representing the neighborhood). Let f (x,t) be the transition function, let N and M be normalizing factors, then we can define n and m as the following integrals over the entire disk (equations 1 and 2 from Rafler [Raf11]):…”

Section: Smoothlifementioning

confidence: 99%

“…The left image in Figure 6 illustrates a SmoothLife glider.5.2. LeniaLenia[Cha19] by Chan expands upon Smoothlife[Raf11] by introducing the kernel K, a composite function, which determines the "texture" and "skeleton" of a creature. The article defines Lenia both in a continuous world suitable for mathematics, as well as in a grid-based world suitable for computations.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Virtual Creature Morphology ‐ A Review

Lai

Leymarie

Latham

et al. 2021

Computer Graphics Forum

View full text Add to dashboard Cite

We present a review of methods for procedurally generating the morphology of virtual creatures. We include a range of methods, with the main groups being from ALife over art to video games. Even though at times these groups overlap, for clarity we have kept this distinction. By including the word virtual, we mean that we focus on methods for simulation in silico, and not physical robots. We also include a historical perspective, with information on methods such as cellular automata, L-systems and a focus on earlier pioneers in the field. CCS Concepts• Applied computing → Computational biology; • Hardware → Biology-related information processing; • Software and its engineering → Interactive games; • Computing methodologies → Artificial life;

show abstract

Section: Smoothlifementioning

confidence: 99%

Section: Smoothlifementioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Virtual Creature Morphology ‐ A Review

Lai

Leymarie

Latham

et al. 2021

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…Previous efforts to build artificial worlds include individual machine code programs competing for computational resources [28], [33], simulated creatures in physics simulators [41] [42] [56] [46], games [7], [16], [45], [48], or abstract worlds [44]. I find the open-ended universes based on cellular automata such as SmoothLife, Lenia, and genelife [6], [25], [30] particulary interesting. CA simulations are an attractive substrate for open-ended environments because they are not based on a facsimile of the physics of our own universe, nor are they an ad-hoc or abstract landscape.…”

Section: Related Workmentioning

confidence: 99%

Carle's Game: An Open-Ended Challenge in Exploratory Machine Creativity

Davis

2021

Preprint

View full text Add to dashboard Cite

This paper is both an introduction and an invitation. It is an introduction to CARLE, a Life-like cellular automata simulator and reinforcement learning environment. It is also an invitation to Carle's Game, a challenge in open-ended machine exploration and creativity. Inducing machine agents to excel at creating interesting patterns across multiple cellular automata universes is a substantial challenge, and approaching this challenge is likely to require contributions from the fields of artificial life, AI, machine learning, and complexity, at multiple levels of interest. Carle's Game is based on machine agent interaction with CARLE, a Cellular Automata Reinforcement Learning Environment. CARLE is flexible, capable of simulating any of the 262,144 different rules defining Life-like cellular automaton universes. CARLE is also fast and can simulate automata universes at a rate of tens of thousands of steps per second through a combination of vectorization and GPU acceleration. Finally, CARLE is simple. Compared to high-fidelity physics simulators and video games designed for human players, CARLE's two-dimensional grid world offers a discrete, deterministic, and atomic universal playground, despite its complexity. In combination with CARLE, Carle's Game offers an initial set of agent policies, learning and meta-learning algorithms, and reward wrappers that can be tailored to encourage exploration or specific tasks.

show abstract

“…The Game of Life (GoL) is a discrete dynamical system, proposed by Conway in 1970. Lenia follows simpler generalizations of GoL, such as "Larger than Life" [4], [5], "RealLife" [9], and "SmoothLife" [11].…”

Section: Introductionmentioning

confidence: 99%

Existence of Life in Lenia

Calcaterra¹,

Boldt²

2022

Preprint

View full text Add to dashboard Cite

Lenia is a continuous generalization of Conway's Game of Life. Bert Wang-Chak Chan has discovered and published many seemingly organic dynamics in his Lenia simulations since 2019. These simulations follow the Euler curve algorithm starting from function space initial conditions. The Picard-Lindelöf Theorem for the existence of integral curves to Lipschitz vector fields on Banach spaces fails to guarantee solutions, because the vector field associated with the integro-differential equation defining Lenia is discontinuous. However, we demonstrate the dynamic Chan is using to generate simulations is actually an arc field and not the traditional Euler method for the vector field derived from the integro-differential equation. Using arc field theory we prove the Euler curves converge to a unique flow which solves the original integro-differential equation. Extensions are explored and the modeling of entropy is discussed.

show abstract

Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife

Abstract: We present what we argue is the generic generalization of Conway's "Game of Life" to a continuous domain. We describe the theoretical model and the explicit implementation on a computer.

Cited by 3 publications

References 0 publications

Virtual Creature Morphology ‐ A Review

Virtual Creature Morphology ‐ A Review

Carle's Game: An Open-Ended Challenge in Exploratory Machine Creativity

Existence of Life in Lenia

Contact Info

Product

Resources

About