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Deep Zoom Perturbation

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Bradley Brown edited this page Aug 13, 2026 · 1 revision

Deep-Zoom Perturbation & Navigation — Model, Tools, Findings

Single reference for how deep-zoom Mandelbrot rendering and interactive navigation work here, why they behave the way they do at extreme depth, and the headless tools that measure it. Read this before touching the deep-zoom render or input path — it exists so the multi-session investigation behind it never has to be repeated. Related plan items: SM-2, SM-5..SM-11 in Open-Work-Plan.md. Memory: project_detail_depth_limit, project_viewcamera_input, project_wave214_qdfloor.

1. Coordinate & precision tiers

  • View centre is carried at octuple-double (OD, ~124 digits) ALWAYS, in FractalViewState (16 limbs) via DeepComplex / ViewCamera. Never reintroduce a plain-double centre with a promotion threshold — that was the historic "anchor drift" bug (frozen ~1e-16 world error blooming ∝ zoom). See project_viewcamera_input.
  • Precision types: DD (Hi/Lo, ~31 digits), QD (X0..X3, ~62), OD (X0..X7, ~124), all in Abstractions/Math. FromCenterOffset(centre, pixelOffset, scale) builds a pixel's coordinate; OD's must use the OD+double full-cascade add ((centre + offHi) + offLo), not OD+OD — the sloppy OD+OD add loses a deep offset past ~1e64 (SM-6).
  • Thresholds (MandelbrotCalculator): QDZoomThreshold=1e25 (QD reference orbit), ODZoomThreshold=1e50 (OD reference orbit). One scale formula everywhere: scale = 3.5 / (max(pxW, pxH) · zoom). Input and render MUST agree on it (ViewCamera.PlaneExtent = 3.5).

2. How a deep frame is rendered (perturbation)

One reference orbit is computed at the view centre in QD/OD and stored to 8 limbs per iteration (_refZr/_refZrLo/..X7). Each pixel iterates only its delta δ = z − Z (perturbation): δ_{n+1} = 2·Z_n·δ_n + δ_n² + dc, where dc = pixelOffset·scale. The full value for the escape test is z = Z_n + δ_n.

  • δ stays in double. δ is a small deviation, so double's exponent range handles it at any depth; only the reference and centre need many digits.
  • Rebasing (SM-2, ComputePixelPTRebased, default on). When δ grows past the full value (|z| < |δ|) or the reference is exhausted, restart the reference (Z[0]=0, δ := z, m := 0). Keeps the δ-chain glitch-free to arbitrary depth without the slow per-pixel QD/OD fallback. The SIMD PT path (ComputeRowPT4/8) carries most pixels; ComputePixelPTRebased is the scalar fallback for lanes that glitch (typically a few % at extreme zoom).
  • SA (series approximation) + BLA skip early/at-scale iterations. Toggle off with DisableAcceleration / DisableSeriesApproximation for A/B.

3. The detail-depth floor (SM-7) — NOT a bug

Perturbation resolves a pixel only while its offset δ (∝ 1/zoom), amplified by ∏|2·Zₙ| over the reference orbit, reaches O(1). If the centre's orbit escapes at iteration N, amplification is finite — Σ log₁₀|2·Zₙ| (frozen at |Z|>2) decades — so zoom beyond ~10^that collapses the whole viewport to one escape value (flat frame). This is a property of the location, not precision: to go deeper, recentre on a point whose orbit stays bounded longer.

  • Exposed as MandelbrotCalculator.MaxUsefulZoomLog10 (+∞ if the orbit stays bounded to maxIter), computed free in every reference-orbit build.
  • Surfaced in the perf-HUD render-context block (ShowPerfHud) as max-detail zoom: ~1eNN plus a yellow warning when the live zoom exceeds it. NOT on the status bar (a long wrapping string there bounced the panel — SM-8).
  • If the user reports "controls break past 1eNN," FIRST check zoom vs maxUseful in the overlay. zoom > maxUseful ⇒ flat dead-zone, expected.

4. Navigation (input) is provably exact — do not re-investigate

All 2D pan / zoom / focus / box-zoom goes through ViewCamera + DeepComplex (OD centre). --inputprobe (headless, to 1e70) and the input-math check in --navrepro show the controller places the new centre to 9.5e-15 px of the ideal OD value at 4.65e64 — i.e. machine-exact, path-independent. The input layer is not the source of any deep-zoom navigation complaint. Native input (NativeMouseForwarder) feeds device-px coords AND device-px client dims (GetClientSize), and the render buffer is device-px, so there is no HiDPI scale mismatch (it cancels).

5. The deep-zoom navigation symptom (SM-11) — RESOLVED: render is consistent

Symptom (user): past ~1e63–1e64, double-click / outline-zoom "get close but not exact" and click-drag pan makes the image "jump around" as the mouse moves.

Conclusion after full measurement: the navigation core is SOUND. Input is exact (§4). The render is reference-consistent during navigation — it does NOT meaningfully redraw the same region differently as the centre moves.

The trail (kept so it is not re-walked):

  • --navrepro on the user's working 1.32701e63 vs broken 4.65087e64 coords first showed a double-click focus "error" of ~2 px → ~16 px (patch-matched), suggesting a zoom-growing reference-dependence.
  • SM-11a (DD reference + DD δ) implemented (ComputePixelPTRebasedDD) and forced across ALL pixels (--navrepro scalar ddref, rebasedPx=942079/942080): focus-err stayed byte-identical 16 px. Rebasing/SA/BLA on/off: also unchanged. So it was never double-rounding precision (matches the old "DD byte-identical" result).
  • --panjitter (the artefact-free test — consecutive OFF-centre pan frames, fresh reference each frame, compare beyond the pure translation): inter-frame Δiter is only 0 / 1 / 3 / 6 per px at 2 / 8 / 20 / 40 px steps. The render is stable frame-to-frame. SM-11b (reference recycling during the drag) changed nothing (recycle vs fresh identical) — because fresh is already consistent.
  • Therefore the --navrepro 16 px was a measurement artefact: frame B is centred exactly on the clicked point, making it frame B's reference pixel (δ=0, escapes at the reference length) vs a perturbed pixel in frame A — the neighbourhoods differ for that reason, and patch-match on self-similar deep structure locks onto colour noise. It is NOT user-visible positional drift.

So neither SM-11a nor SM-11b was needed. What the user perceives as "close but not exact / jumping" is the residual below, not a navigation fault.

6. What actually remains (cosmetic, deep zoom)

  • ¼-res progressive drag preview. RenderHint.Fast → Trigger(progressive) shows a ¼-then-½-res preview during a drag; the block edges shift as you move, which reads as "jumping" on a busy deep image. This is preview resolution, not navigation. Lever: higher preview floor (½ instead of ¼) at deep zoom, or a brief settle before the first preview.
  • Palette sensitivity. The reference-consistent render still varies by a few iteration counts frame-to-frame (Δiter ≤ ~6/px over a 40px pan); a fast-cycling rainbow palette turns that into visible shimmer. Lever: a less iteration-sensitive / smoothed palette.
  • Both are cosmetic. The reference-recycle plumbing (RecyclePreviewOrbit, default OFF; MandelbrotCalculator.AllowRecycleThisRender) is kept but unused — --panjitter showed it changes neither pixels nor perceptible speed.

If a positional error is ever reproduced on a DETAILED frame, re-open with --panjitter (artefact-free) rather than the --navrepro focus test, and only then consider a QD-δ variant.

7. Diagnostic tools (headless, in Program.cs)

Run dotnet FracturingFog.dll <flag>; each writes a .out next to the exe.

Flag Measures
--inputprobe Controller anchor drift vs OD truth, wheel/click/pan, to 1e70. Expect 0.00 px.
--focusprobe [dim] End-to-end double-click focus px error + frame richness + MaxUsefulZoomLog10 + ref-orbit escape, over a zoom sweep.
--navrepro [file] Reproduce a USER view from a coordinate file (Docs/Nav-Repro-Template.txt): full-limb cx/cy, zoom, dim, click. Reports input-math error, rendered focus-err, SAD(0,0) vs SAD(min), rebased-pixel count, maxUseful. Path toggles: norebase acceloff saoff ddref scalar. NOTE: its focus-err centres frame B on the clicked point (reference-pixel artefact) — use --panjitter for an artefact-free reference-consistency check.
--panjitter [step] Artefact-free render-consistency test: simulate a horizontal drag at a deep centre, compare consecutive OFF-centre frames beyond the pure pan (inter-frame Δiter/px), FRESH vs RECYCLE. Low = render is stable during navigation.
--qdfloorsweep QD/OD coordinate-separation floor (distinct per-pixel coords vs zoom).
--rebaseprobe Rebasing vs QD parity + speedup.

To capture a repro from a user: overlay px WxH, menu full-limb CX/CY, zoom, and roughly where they clicked → Docs/Nav-Repro-Template.txt → --navrepro. The overlay's limbs X:n/8 Y:n/8 shows centre precision at a glance (a truncation bug would drop n).

8. Diagnostic toggles on MandelbrotCalculator (all default off/safe)

  • AllowPtRebasing (default on) — Zhuoran rebasing; "Bypass Rebasing" UI.
  • UseDdRebaseReference — DD reference in the rebased loop (SM-11a, tested insufficient; kept for the QD follow-up).
  • ForceScalarPtPath — bypass SIMD so all pixels hit ComputePixelPTRebased (diagnostic; slow).
  • DisableAcceleration / DisableSeriesApproximation / DisableDdBla.

9. Rules of thumb

  1. Deep-zoom "controls broken"? Check overlay zoom vs maxUseful first (dead-zone), then run --navrepro on the coordinate. Input is exact — look at the render, not the input handlers.
  2. Never re-add per-tier branches to input handlers or a plain-double centre.
  3. New precision tier / zoom backend → extend DeepComplex only.
  4. Keep ComputePixelPTRebased and ComputePixelPTRebasedDD in sync.
  5. Don't put long/variable status text on the status bar (panel resize bounce).

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