OLVERTH / KHENOR • experimental build 0.8
Can a formula become an image?
KHENOR currently searches a mathematical grammar including repeated reflection operators for a formula that approximates the image. The .khen formula alone can regenerate the result without the original file. Exact reconstruction is only claimed when every RGB byte matches.
KHENOR / KH1 mathematical text format
A real equation, not a renamed ZIP file.
KHENOR fits a library of symbolic primitives to the selected image and gives you an executable mathematical description. Formula-only: no hidden pixel payload or compressed photograph. The result may look different; real photos generally need much more information for fidelity.
01 / INPUT
The image selected in the experiment below is used here. Or use a sample or upload a picture in the RRT5 controls.
02 / COMPLEXITY BUDGET
Each term uses one known mathematical primitive and three RGB coefficients. The experimental orbit operators use repeated mathematical reflections: T(z)=1−|2z−1|. More terms can increase fidelity but enlarge the description.
Ready for symbolic search.
Download an example .khen (53 bytes). Its reflection-built test image is reproduced exactly; this is not a real-photograph claim.
I(x,y) = [formula discovery not run]
KH1;...
The .khen file contains a one-line symbolic program with dimensions and coefficients. The 53-byte example requires the shared decoder and grammar, which are not counted in its file size. Most photographs cannot be faithfully represented by so few bytes. A short expression may still give low visual fidelity.
Secondary reference experiment / RRT5
Compare against the existing RRT5 codec.
The algorithm uses compact color planes, exact pixel exceptions, adaptive quadtree partitioning and lossless deflate fallback, with reversible spatial prediction. There is no neural model or claim of universal compression.
Run the separate RRT diagnostic experiment to compare encoded sizes.
The decoder independently verifies a checksum. Exact mode requires pixel-for-pixel identity.
WebP is shown only as a reference, not an equal-quality benchmark: WebP quality is fixed at 0.8, while RRT5 uses its own quality objective. RGB counts exclude the uploaded container and metadata. Decoder code size is not included in encoded file sizes. Images larger than the test limit are explicitly downscaled before analysis, and all comparisons use that same test raster.
Research update / November 2026
Improving the exact path. Not beating WebP yet.
RRT5 adds reversible spatial prediction and cross-channel decorrelation. On one small photographic test raster (192 × 128 pixels), the encoded RGB is 39,978 bytes versus 61,752 bytes for direct deflate; WebP lossless is smaller at 33,178 bytes. Image dimensions and decoder overhead must be included in practical comparisons. These are limited diagnostic measurements, not broad benchmarks.
Research hypothesis
Preserve the rules, not necessarily every sample.
The present model is intentionally simple. A future experimental line will study learned constraints and projection operators while maintaining separate tests for fidelity, semantics and recoverability.
Search for local rules
Fit color fields to parts of an image, rather than treating every pixel as unrelated.
Store deviations only
Preserve sparse counterexamples when a compact rule almost describes the original.
Measure every outcome
Exact mode performs a full pixel comparison. Approximate mode reports distortion and must be judged against strong codecs.