{"slug":"oip-invariant-6-36-scale-invariance-fractals-allometry","title":"Invariant 3.6 — 3.6 Scale invariance / fractals / allometry","body":"# Invariant: 3.6 Scale invariance / fractals / allometry\n\n### 3.6 Scale invariance / fractals / allometry\nThe same rule at every zoom. **Sources:** Mandelbrot; renormalization; Kleiber's law; West, Brown & Enquist (metabolic scaling). **Domains:** coastlines, vasculature, cities, organisms, cosmic web. **Dual:** characteristic-scale systems. **Tier:** T1. **Falsifier:** a branching transport network that violates the scaling exponent. **Maps:** A₇.\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C10](/a/oip-node-c10-scale-invariance-fractals-allometry) · [Encyclopedia C10](/a/convergence-encyclopedia-c10)\n- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)","register":"oip_protocol","tags":["philosophy","oip","catalogue","invariant","systems-theory"],"category":null,"style":{},"claims":[{"id":"c1","text":"Scale invariance is the property that the same rule applies at every zoom level.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"States the core definition of the invariant."},{"id":"c2","text":"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"Lists the empirical domains to which the invariant applies."},{"id":"c3","text":"The dual of scale-invariant systems is characteristic-scale systems.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the contrasting property for the invariant."},{"id":"c4","text":"A falsifier for the invariant is a branching transport network that violates the scaling exponent.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Provides the explicit test condition for the invariant."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}