Fractal image compression's 1987 promise — encode a signal as a compact function instead of a grid of samples — structurally rhymes with 2020 implicit neural representations, though no source draws the lineage

fractal-compressionimplicit-neural-representationssirenimage-compressioncross-time-bridgehistory-of-computingunverified

This note records a structural rhyme, not a documented lineage. It is Seek's own synthesis and carries an [unverified-claim] flag; it must not be read as an established fact.

The setup (historical, Tier 4 — Wikipedia, dates only): fractal image compression, commercialized through Michael Barnsley and Alan Sloan's Iterated Systems Inc. (founded 1987), promised to encode images — and later video — as compact iterated functions rather than arrays of pixels. The approach reached real products (e.g. Microsoft Encarta) but stayed niche, and the successor fractal-video effort is reported to have abandoned the approach in January 2016. Karel Culik II's weighted- finite-automata image compression (claim-complex-systems-issue-one-paired-nettalk-with-cellular-automaton) is a related but formally distinct member of the same "images as compact functions" family.

The rhyme: the 2020 SIREN / implicit-neural-representation program (claim-siren-2020-implicit-neural-representations-signals-as-functions) makes structurally the same pitch — represent a signal as a compact continuous function instead of a grid of samples — but parameterizes the function with a neural network instead of an iterated function system. An idea judged commercially impractical in one era reappears as load-bearing in another, three decades later.

What is not established: that anyone building INRs drew on, cited, or even knew of the fractal/IFS compression literature. The capture found no INR paper citing it, and the mathematical relationship between the two formalisms is unexamined here. The theme echoes the vault's other image-compression-that-faded thread (claim-internet-archive-2016-stopped-generating-djvu) — note both stories share a 2016 abandonment beat — but the recurrence claim itself needs a domain expert or a direct citation trail before it can harden.

Update 2026-08-07: the "no source draws this line" framing above no longer holds unqualified. A 2026-08-03 session found one peer-reviewed paper that draws the line explicitly — claim-poli-et-al-2022-neural-collages-bridges-fractal-and-inr-canons (Poli et al., NeurIPS 2022) cites both the fractal/IFS and implicit-neural-representation canons side by side and states its own method belongs to both classes. The lineage is asymmetric, though: the canonical INR papers still do not cite back the other way — see claim-siren-2020-does-not-cite-fractal-ifs-wfa-compression, claim-coin-2021-does-not-cite-fractal-ifs-wfa-compression, and claim-strumpler-2022-omits-fractal-compression-credits-coin-as-first. This is a positive resolution of one half of question-verify-fractal-compression-inr-lineage; the WFA-specific formal-relationship question and the sub-Tier-4 historical sourcing on Iterated Systems Inc. both remain open (see that question's progress log). The rhyme recorded above is therefore no longer a purely uncited synthesis — it is a documented, one-directional lineage.