![\"Directing](\"https:\/\/www.newsbeep.com\/il\/wp-content\/uploads\/2026\/06\/Directing-Open-Ended.png\")
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\n Pipeline: Lagrangian tracking \u2192 \ud835\udc3b\u0394\ud835\udc61 heatmap \u2192 MSPD aggregation \u2192 evolutionary loop \u2192 complex simulation output. \u2014 cs.NE <\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
High-HDeltat 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..<\/p>\n
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.<\/p>\n
Mikhail Akhtyrchenko, Mikhail I. Katsnelson, Andrey Ustyuzhanin<\/p>\n
Subjects: Neural and Evolutionary Computing (cs.NE); Statistical Mechanics (cond-mat.stat-mech); Cellular Automata and Lattice Gases (nlin.CG) Astrobiology,<\/p>\n","protected":false},"excerpt":{"rendered":"Pipeline: Lagrangian tracking \u2192 \ud835\udc3b\u0394\ud835\udc61 heatmap \u2192 MSPD aggregation \u2192 evolutionary loop \u2192 complex simulation output. \u2014 cs.NE…\n","protected":false},"author":2,"featured_media":509152,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[345,233850,233851,5351,85,46,233852,233853,148386,141],"class_list":["post-509151","post","type-post","status-publish","format-standard","has-post-thumbnail","category-science","tag-ai","tag-artificial-life","tag-darwinian-cellular-automata","tag-evolution","tag-il","tag-israel","tag-multi-scale-path-divergence","tag-open-ended-evolution","tag-origin-of-life","tag-science"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/509151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/comments?post=509151"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/509151\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media\/509152"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media?parent=509151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/categories?post=509151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/tags?post=509151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Cite as: arXiv:2606.17091 [cs.NE] (or arXiv:2606.17091v1 [cs.NE] for this version)
https:\/\/doi.org\/10.48550\/arXiv.2606.17091<\/a>
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Submission history
From: Andrey Ustyuzhanin
[v1] Fri, 12 Jun 2026 22:24:12 UTC (2,695 KB)
https:\/\/arxiv.org\/abs\/2606.17091<\/a><\/p>\n