  The relationship between reaction-diffusion (RD) systems, characterized by
continuous spatiotemporal states, and cellular automata (CA), marked by
discrete spatiotemporal states, remains poorly understood. This paper delves
into this relationship through an examination of a recently developed CA known
as Lenia. We demonstrate that asymptotic Lenia, a variant of Lenia, can be
comprehensively described by differential equations, and, unlike the original
Lenia, it is independent of time-step ticks. Further, we establish that this
formulation is mathematically equivalent to a generalization of the
kernel-based Turing model (KT model). Stemming from these insights, we
establish that asymptotic Lenia can be replicated by an RD system composed
solely of diffusion and spatially local reaction terms, resulting in the
simulated asymptotic Lenia based on an RD system, or "RD Lenia". However, our
RD Lenia cannot be construed as a chemical system since the reaction term fails
to satisfy mass-action kinetics.
