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Universal self-replicator in Lenia or related kinetic models

Construct a universal self-replicator within Lenia or a closely related continuous cellular automaton/kinetic model, demonstrating non-trivial self-replication and Turing-universal computation within that substrate.

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Background

The paper discusses Lenia and related continuous-space CA-like systems, noting their rich life-like dynamics but arguing that currently observed replication-like behaviors may be more akin to particle splitting than genuine universal self-replication.

They conjecture that a universal self-replicator could be built within Lenia, extending CA-based replication insights to kinetic models.

References

We also venture the following conjecture: Conjecture It is possible to build a universal self-replicator within Lenia (or one of its natural variants).

— Self-replication and Computational Universality (2510.08342 - Cotler et al., 9 Oct 2025) in Section 'Open problems and conjectures' (Kinetic models)