Definition. One splat
A splat is a Gaussian: a center μ and a covariance Σ. It is a soft ellipse with no edge, brightest in the middle and fading as exp(−½ d2), where d counts standard deviations from the center.
Σ = R S STRT = 2.010.720.720.60
R = 0.91−0.420.420.91 S = 1.50000.60 det Σ = 0.810
Renderers store Σ as a rotation R and a scale S because any pair of them gives a valid covariance, so an optimizer can move them freely. In three dimensions a splat gains a third axis, an opacity and a color; the renderer projects each one onto the screen, sorts them by depth and blends (Kerbl et al., 2023).
Splashery’s Tinkerer’s Manual teaches this level by level: what one splat is, how a recipe is built, and a splat equation language.
Lemma. Splitting loses nothing
However a splat’s pixels are divided, the two halves carry the parent’s mass, mean and covariance between them.
Σ = w1(Σ1 + δ1δ1T) + w2(Σ2 + δ2δ2T), δk = μk − μ
Each half brings two things: its own spread, Σk, and the offset of its center from the parent’s, δk. Weighted by its share of the pixels, wk, they add up to the parent again.
The two halves, put together
- pixels
- 0 + 0
- mean
- (0.0, 0.0)
- inside
- 0000
- between
- 0000
- sum
- 0000
The splat, measured whole
- pixels
- 0
- mean
- (0.0, 0.0)
- Σ
- 0000
Relative error: 0
Proof. By checking. All 16,383 splits behind the picture at the top of this page hold, with a worst relative error of 0. A test suite checks 169,544 more on bars, rings, diagonals and dust, recomputes every node from its raw points, and tries 11,200 divisions that are not at the median: straight cuts at any angle, and divisions with no shape at all. ∎
The name is fitted by moment matching: each splat is the exact mean and covariance of the pixels it stands for, and each split falls at the median along the long axis. Real Gaussian splatting fits by gradient descent. Splashery has a toy that shows it, next.
Example. Splashery
Splats you can play with.
A playground of 3D Gaussian splats that runs entirely in the browser: captured objects of up to 450,000 splats, and generated ones built from seeded recipes. Every effect (poke, wind, dissolve, drop, magnet, twist, slice, paint) runs on the GPU for every splat, every frame; the CPU only sets a few uniforms.
My part: I defined the project’s vision and its toy categories, refined the interaction design through hands-on testing, and contributed mathematical recipes.
Further examples. Other work
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grooph
Visual loop graphs for coding-agent workflows. You draw who builds, who checks, where a person decides and when the work stops. grooph checks that every loop names a stop, then compiles the graph into a prompt package for a separate coding-agent harness. It runs no agent and calls no model, and graphs stay on your device.
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aqrobat
A local text and emoji QR lab. Give it a link or a little text and it builds QR artwork from letters, symbols or emoji, in the browser.
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Ars Magna
An anagram finder. Give it any text and it returns every way those exact letters can be re-partitioned into real English words, by a deterministic search.
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Amordle
A free word game: any word length from 2 to 35 letters, three difficulties, a daily puzzle, and ranked multiplayer with an Elo rating.
See also
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reword_nerd
A local-first browser workbench that turns a reviewed document, or a set of images, into a portable workbook of rewriting prompts. Everything stays reviewable in the browser, the download is a separate, explicit step, and the application contacts no model provider itself.
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resmon
A local-first literature-monitoring desktop application. It runs scheduled searches across open-access scholarly sources, removes duplicates, and compiles reading reports, with optional summaries.
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Link Meteor
A Chrome extension that collects links with their anchor text and URL in separate fields, for reviewing sources and exporting a research collection. No account, ads, telemetry or backend.
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English OpenList
A free, open, continuously maintained list of valid English words, about 345,000 of them, with the provenance of every word (which sources attested it, and when), auditable correction records, and a browser explorer.
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The Speed-Accuracy Trade-Off in Perceptual Decision-Making
Evidence accumulation modeled as a diffusion process, with dynamic programming and value iteration to study decision boundaries in a simulated obstacle-avoidance scenario. My undergraduate research capstone, April 2025.
Everything public is on the repository map.