---
title: "Collage Theorem"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Collage Theorem"
aliases: []
first_seen: "2026-08-03T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["fractal compression","Michael Barnsley","Neural Collages","implicit neural representations","iterated function systems"]
seek_code_commit: "649b1a4"
---


A 1985 result in fractal geometry, proved by Michael Barnsley and Stephen Demko, showing that an iterated function system's attractor can be made arbitrarily close to a target image by choosing contraction maps that each place a scaled copy of the whole image close to a piece of itself. It converted fractal self-similarity from a descriptive curiosity into a constructive compression method: find the collage, and you have encoded the image.

Matters to this vault as the specific mathematical hinge Poli et al.'s 2022 Neural Collages paper reframes as a differentiable, hypernetwork-trained operator — the concrete technical object underneath this vault's citation-lineage finding that fractal compression and implicit neural representations are, in one documented instance, treated as the same class of method.

## References
- [[claim-poli-et-al-2022-neural-collages-bridges-fractal-and-inr-canons]]
- [[entity-michael-barnsley]] · [[entity-michael-poli]]