Genesis: An Empirical Platform for Studying Open-Ended Evolution Without Fitness Functions

Can evolutionary dynamics characteristic of biological development arise without a designer-specified fitness function? We present Genesis, a platform in which agents inhabit a Gray-Scott reaction-diffusion substrate and evolve under physical constraints alone. Three successive experimental cycles, each testing one falsifiable hypothesis, show: (1) constraint-driven selection sustains evolutionary activity after complete fitness removal but reaches a hard phenotypic complexity ceiling; (2) agent-mediated niche construction via chemical secretion is real but causally insufficient to break that ceiling; and (3) replacing the fixed-alphabet genome with a Compositional Pattern Producing Network (CPPN) indirect encoding, protected by NEAT-style speciation, produces the first evidence of progressive structural complexification in a fitness-free system. Null results are treated as precise, informative answers rather than failures, yielding reusable diagnostic tools and a sham-control protocol applicable to any open-ended evolution evaluation pipeline.

Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.

Open-ended evolution (OEE) in artificial life is typically driven by uninterpretable, black-box neural-network complexity metrics, leaving life-like systems disconnected from physical theories of complexity. We introduce MSPD (Multi-Scale Path Divergence, denoted DP ), a renormalization-group-inspired scalar that quantifies the temporal multiscale organization of heterogeneity in local transition laws. MSPD is defined at the population level as a functional of the realised trajectory and is computed as a windowed finite-resolution estimator, with consistency between the two stated as a proposition. The metric is an explicit formula and plays a dual role: as a gradient-free fitness function and as a post-hoc analytical lens on any simulation that exposes local transition laws. Empirically, MSPD-optimized parameters produce higher held-out complexity scores than matched random parameters from the same substrate. High-$H_{Delta_t}$ states correspond to states with higher instability to external interventions, so the metric tracks the biology of the underlying dynamics rather than noise. Higher MSPD corresponds to stronger scale-dependent frustration: high-complexity systems exhibit larger differences between the dynamics expressed at different spatial extents, linking MSPD directly to the frustration criterion of biological complexity in the sense of Vanchurin et al. [ 23 ]. The same protocol transfers beyond the primary Flow-Lenia substrate to Life-like cellular automata and Particle Life++, where C1, C2 and C5 all hold. A single explicit formula thus both directs open-ended evolution and provides a principled bridge to the physics of complexity that black-box drivers do not.