Research paper · release 0.1
Fractapp FIC/5: Fractal-Addressed, Locally Decodable Lossless Image Storage
Abstract
Fractapp investigates whether recursive integer-addressed geometry can serve as a useful logical substrate for storage and local retrieval. FIC/5 uses one mathematically implied 64×64 image grid, direct region access, exact block reuse, and per-block reversible transform selection with a conventional fallback. The frozen balanced profile passed its declared public-split targets and then a subsequently opened H2 holdout. On the public photographic split it measured 0.658× median total-package size, 0.967× crop payload, 0.975× cold-object crop bytes, and 0.705× crop decode time relative to the strongest exact-deduplicated complete 64/128/256 tile-pyramid baselines in the experiment. H2 measured 0.512×, 0.830×, 0.848× and 0.419× respectively, with exact pixel reconstruction. The result is bounded to the committed corpus, normalization, implementation and baselines.
1. Core separation
The central design decision is to separate logical geometry from physical representation. The recursive Base-4 address says where an image region belongs and which larger regions contain it. The payload says how the information needed for that region is reversibly represented. Physical bytes remain tightly packed. The fractal is the map, not a literal scattering of bytes through geometric coordinates.
2. FIC/5 node representation
Each 64×64 region evaluates nine reversible candidates: raw RGBA, row XOR, PNG-like Sub, Paeth, green-difference decorrelation, XOR after green-difference, planar RGBA, planar green-difference, and Sub after green-difference. The balanced profile chooses a fast transform when its payload lies within 2.5% of the smallest candidate.
3. Random access
A crop resolves to the logical nodes intersecting its rectangle. Only corresponding physical payloads and necessary index material are counted as touched. The reconstructed crop is compared with the authoritative source crop by SHA-256.
4. Public result
| Metric | Ratio | Meaning |
|---|---|---|
| Total package | 0.658× | 34.2% smaller |
| Incremental crop payload | 0.967× | 3.3% fewer bytes |
| Cold-object crop | 0.975× | 2.5% fewer bytes |
| Decode time | 0.705× | 29.5% faster in recorded Vercel run |
5. Frozen H2 holdout
After candidate source and parameters were frozen, H2 was opened once and consumed. No predictor, transform set, tile size, baseline, profile, or metric was changed after opening.
| Metric | Ratio | Meaning |
|---|---|---|
| Total package | 0.512× | 48.8% smaller |
| Incremental crop payload | 0.830× | 17.0% fewer bytes |
| Cold-object crop | 0.848× | 15.2% fewer bytes |
| Decode time | 0.419× | 58.1% faster in that run |
6. Negative results mattered
FIC/2 won on a structural synthetic image but did not generalize. FIC/3 achieved strong whole-object storage but missed local-access and decode parity. FIC/3.1 added alternate routes and regressed access. FIC/4 explored a dictionary-backed mixed quadtree. The champion emerged by returning to a simpler fixed address grid and improving reversible local representation.
7. Claim boundary
8. Next work
H2 is consumed. A new holdout must be sealed before optimization. Candidate directions include reversible MED/JPEG-LS-style prediction, YCoCg-R-class decorrelation, row-adaptive prediction, block-local entropy coding such as rANS, and real HTTP range retrieval proving only requested regions cross the network.
9. Authorship
Jonathan H. Lindley originated and directed the program and is the responsible human author. ChatGPT contributed algorithm design, engineering, benchmark design, analysis and drafting as an AI co-author. This does not imply OpenAI review or endorsement.