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Fractal Expansion Roadmap
Future work plan. Each family below is not yet rendered by Fracturing Fog as of v0.6.x. Grouped by engine reuse — items in same phase share infrastructure.
Existing extension points to reuse:
-
IFractalKernelstruct-generic kernel (seeFRACTAL_EXPANSION_PROMPTS.mdPrompt 0) -
FractalParametersrecord for per-family params - CalcGen 5-path pipeline (scalar / AVX2 / Pert / BLA / ILGPU) — auto-applies once kernel registered
- 3D pipeline:
UserBulbraymarcher +Vec3/Quattriplex algebra - Theme system gates interior-cycle themes per FractalType; smooth-iter + distance themes work on any escape-time kernel
Reuse existing IFractalKernel + per-pixel iteration loop. Each = one struct file + Type combo entry + Help → Mathematics tab. No new pipeline.
- Formula:
z = ((z² + c - 1) / (2z + c - 2))² - Rational map; bailout 10² (slower grow), needs divide-safe Step
- Risk: pole at
2z + c - 2 = 0— clamp denom magnitude in Step - Params: none beyond c
- Deliver:
MagnetOneKernel.cs, Type combo, Math help tab, 1 region preset
- Formula:
z = ((z³ + 3(c-1)z + (c-1)(c-2)) / (3z² + 3(c-2)z + c² - 3c + 3))² - Same risk as A.1; bigger expression
- Deliver:
MagnetTwoKernel.cs, Type combo, Math tab
- Iterate Halley's method on user polynomial (default
z³ - 1) - Step:
z -= 2f·f' / (2f'² - f·f'') - Reuses Newton's
NewtonPolyCoeffsparam + derivative cache - Deliver:
HalleyKernel.cs, polynomial param picker shared with Newton, Math tab
- Two-point recurrence
z_{n+1} = z_n - f(z_n)·(z_n - z_{n-1}) / (f(z_n) - f(z_{n-1})) - Needs prev-z slot — model after
PhoenixKernelwhich already keeps prev - Deliver:
SecantKernel.cs, Math tab
- Formula:
z = z^1.5 + cwithc ≈ -0.2 - Fractional power → use
Complex.Pow(log/exp) - Deliver:
GlynnKernel.cs, default region at canonical Glynn coords
- Two-state recurrence:
z = z² + c; c = c/2 + z - c mutates per iteration —
IFractalKernel.Stepneedsref cx, ref cyoverload, OR new sub-interfaceIMutatingKernel - Architecture cost: small — add overload; existing kernels ignore
- Deliver:
SpiderKernel.cs, kernel-interface extension, Math tab
- Not escape-time. 1D map
x_{n+1} = r·x_n·(1 - x_n) - Render: x-axis = r (3.0 – 4.0), y-axis = settled-x density
- Needs own renderer path — histogram accumulator like Buddhabrot
- Reuse: Buddhabrot's accumulation buffer + log-density tone-map
- Deliver:
LogisticRenderer.cs(sits alongsideBuddhabrotRenderer), Type combo, Math tab - Themes: density-histogram only; gate interior themes off
Phase A exit: 7 new 2D families, no new pipeline beyond kernel-interface mutating-c overload + bifurcation density renderer.
Reuse UserBulb raymarcher (DE-based sphere tracing, normal estimation, lighting). Add new fold-style DE functions.
- Box-fold + sphere-fold + scale:
z = scale · sphereFold(boxFold(z)) + c - Tunables: scale (default 2.0; ≈ -1.5 / 2.0 / 3.0 are classics), fixedRadius (1), minRadius (0.5)
- DE:
length(z) / |dz|with dz tracked through folds - ILGPU: straightforward — folds are conditional negate/scale, no transcendentals
- Deliver:
MandelboxKernel.cs(3D), MandelboxParams struct, 4 region presets (-1.5, 2, 3, +negative scale), Math tab - Risk: scale near critical values blows up — clamp iters, raise bailout
- Repeated fold + scale-from-pivot. Menger: 3 axis-folds + scale-3 from (1,1,1). Sierp tetra: 4 vertex reflections + scale-2.
- DE:
(length(z) - constant) / scale^n - Tunables: iteration count, scale, pivot, rotation matrix
- Two presets share single
KifsKernelparameterized by fold table - Deliver:
KifsKernel.cs, 2 built-in fold-table presets (Menger / Sierp), Params dialog tab, Math tab
- Reuse User Bulb's chain editor — already lets user stack multiple Step functions
- Action: register Mandelbox-fold + KIFS-fold + Mandelbulb-power as chain primitives in
UserBulbChainPrimitives.cs - Users compose hybrids without code; promoted entries become Type-combo fractals
- Deliver: 3 chain primitives + 2 worked-example chains shipped as built-ins
- Low risk — leverages existing system
- Iterated Möbius transforms (sphere inversions) in 3D
- Complex math — defer behind B.1–B.3
- Deliver:
KleinianKernel.cs, params = inversion-sphere list (radius + center per sphere), 1 preset (Apollonian-style packing)
Phase B exit: 4 new 3D families + Mandelbulber-class composability.
New algebra layer. Mandelbulb's triplex won't suffice — need true 4D number types.
-
q_{n+1} = q_n² + c, q ∈ ℍ - Reuse existing
Quatfrom User Bulb 4D mode - Render: raymarch a 3D slice (fix one quaternion component as "slice w")
- UI: Params dialog adds slice-w slider — live re-render
- Deliver:
QuatJuliaKernel.cs, slice-w param, 3 classic c presets (-0.2+0.4i+0.4j+0.4k, etc.), Math tab
- Same algebra, vary c per pixel
- Deliver:
QuatMandelbrotKernel.cs, slice picker, Math tab - Share raymarch infra with C.1
- Tessarine algebra (commutative, zero-divisors present)
- New
Bicomplexstruct inAbstractions/Numerics/ - Deliver:
Bicomplex.cs,BicomplexMandelbrotKernel.cs, slice picker, Math tab - Lower priority — visually similar to quat in many slices
Phase C exit: True 4D fractals with interactive slice control.
These don't fit escape-time. Each needs dedicated renderer.
- Circle packing via Descartes Circle Theorem
- Recursive: from 3 mutually tangent circles, generate 4th, recurse
- Renderer: tree traversal until circle radius < pixel
- Deliver:
ApollonianRenderer.cs, depth-limit param, color-by-depth, 2D only, Math tab
- Stochastic. Seed pixel; random-walk particles stick on contact
- Renderer: simulate N particles, accumulate hit map
- Determinism: seedable PRNG; cache result per (seed, N, region) — slow to compute
- Deliver:
DlaRenderer.cs, particle-count + seed params, color-by-arrival-time, Math tab - Risk: zoom non-trivial — pre-render at fixed grid; pan/zoom = blit cached buffer until re-sim
- Don't support: pan/zoom-aware live re-sim (deferred)
- Procedural noise terrain — not strictly fractal but renders as one
- Renderer: square-step + diamond-step over 2D grid, recursive midpoint displacement
- Deliver:
PlasmaRenderer.cs, roughness + seed params, 2D, Math tab - Themes: full gradient palette works directly
- IFS + per-map non-linear "variation" + log-density tone-map
- Reuse existing IFS pipeline; extend
AffineMap→FlameMapadding variation enum (linear, sinusoidal, spherical, swirl, horseshoe, polar, handkerchief, heart, disc, spiral, hyperbolic, diamond, ex, julia, bent, waves, fisheye, popcorn, exponential, power, cosine, rings, fan, blob, pdj, fan2, rings2, eyefish, bubble, cylinder, perspective, noise, juliaN, juliascope, blur, gaussian, radial-blur, pie, ngon, curl, rectangles, arch, tangent, square, rays, blade, secant, twintrian, cross — Apophysis stock set, 49 variations) - Initial cut: 8 most-used variations (linear, sinusoidal, spherical, swirl, polar, heart, disc, julia)
- Renderer: chaos game + log-density accumulation + gamma tone-map
- Deliver:
FlameRenderer.cs,FlameMap.cs, variation enum + lookup, 6 built-in flame presets, Math tab, theme integration via density palette - Big phase. Plan as 3 slices: core chaos-game → variation library → tone-map + palette.
- All L-System representable. Confirm before building dedicated path — likely just add new L-System presets.
- Deliver: 5 new L-System presets in built-in library, no code change beyond preset JSON
Phase D exit: Stochastic + geometric coverage; flame fractals = biggest user-visible feature.
| Order | Phase | Why this slot |
|---|---|---|
| 1 | A.1 + A.2 Magnet 1/2 | Single-file kernels, classic missing pair |
| 2 | A.7 Logistic | Reuses Buddhabrot accumulator, big visual variety |
| 3 | A.3–A.6 Halley/Secant/Glynn/Spider | Batch the small kernels |
| 4 | B.1 Mandelbox | Highest user-impact 3D add; well-trodden |
| 5 | B.3 Hybrid chain primitives | Leverages B.1 + existing User Bulb |
| 6 | B.2 KIFS | Menger / Sierp recognizable shapes |
| 7 | C.1 Quat Julia | Reuses Quat from User Bulb 4D |
| 8 | D.5 L-System presets | Cheap shipping win |
| 9 | D.3 Plasma | Simple renderer, broad appeal |
| 10 | D.4 Flame fractals | Largest phase; 3 sub-slices |
| 11 | C.2 Quat Mandelbrot | Pairs with C.1 |
| 12 | D.1 Apollonian | Niche but iconic |
| 13 | B.4 Kleinian | Complex; do after flame infra settles |
| 14 | C.3 Bicomplex | Lowest visual differentiation vs C.1/C.2 |
| 15 | D.2 DLA | Stochastic — caching complexity |
Each new family needs entry in theme-gating table. Default rules:
- Smooth-iter + distance themes: enable on all escape-time families (A.1–A.6, B.1–B.4, C.1–C.3)
- Interior cycle themes: Mandelbrot-only (existing rule, no change)
- Density-histogram themes: enable on A.7, D.2, D.4
- 3D Phong / PBR themes: enable on B.* + C.* only when DE + normal estimation present
Each new family = one new sub-tab. Current count: 18. Post-roadmap: ~33. Reorder Math tab as 2-level (Family group → specific tab) once > 25.
Each family ships ≥ 1 built-in region. Total new built-ins: ~25.
Phase A families that fit f(z, c) shape (A.1, A.2, A.5, A.6) should auto-flow through CalcGen 5-path generator. Verify per-kernel; bailout-radius + cardioid-skip differ.
No new JSON files. Existing regions.json + colorthemes.json cover everything.
Each FractalType added to enum becomes immediately addressable from --batch --fractal=.... Audit batch help text after each phase.
User-code families stay blocked. New built-ins (A–D) are server-safe — whitelist in Server/FractalGuard.cs per phase.
- Mandelbar — = Tricorn, already shipped
- Cubic / Quartic Mandelbrot — covered by Multibrot exponent param
- Strange attractor variants (Lorenz, Rossler, Clifford, De Jong, Pickover) — already shipped under StrangeAttractor
- Buddhabrot variants (Nebulabrot, anti-Buddhabrot) — extend existing Buddhabrot, not new family
- Pickover stalks, orbit traps — coloring, not fractals; live in theme system
- Cantor set, Koch — too trivial as standalone; L-System covers
| Risk | Mitigation |
|---|---|
| Magnet pole instability | Denominator-magnitude clamp; bailout 10² not 4 |
| Mandelbox scale critical points | Iter clamp + diagnostic overlay in dev |
| Flame fractal scope creep | 3-slice plan: core / variations / tone-map. Ship slice 1 even if 2/3 deferred. |
| DLA pan/zoom UX | Render to fixed grid; live re-sim deferred |
| 4D slice UI complexity | Single slice-w slider in Params dialog; defer arbitrary-plane slicing |
| Theme combinatorial explosion | Auto-gate via family-tag set on each theme + family |
| Math help tab proliferation | Two-level grouping after count > 25 |
- Branch per phase:
feature/fractals-phase-a, etc. - Each family = own slice commit within phase branch (mirrors current
Cross-platform: Phase X.2 Slice N.Mconvention) - FEATURES.md "20+ fractal families" line updates per phase
- README badge counter for fractal count
Implementation landed on feature/cross-platform-full rather than the
per-phase branches originally planned — all 15 slices in the recommendation
table merged sequentially into one branch.
| Slice | Status | Commit | Notes |
|---|---|---|---|
| A.1 Magnet 1 | ✅ | (Phase A bundle) | |
| A.2 Magnet 2 | ✅ | (Phase A bundle) | |
| A.3 Halley | ✅ | 44ff899 |
|
| A.4 Secant | ✅ | f2a26d2 |
|
| A.5 Glynn | ✅ | (Phase A bundle) | |
| A.6 Spider | ✅ | 9b87e83 |
Adds IMutatingKernel overload for ref-c kernels |
| A.7 Logistic | ✅ | (Phase A bundle) | Density-histogram renderer alongside Buddhabrot |
| B.1 Mandelbox | ✅ | 43d57e7 |
Includes AnyCPU standardisation + 3D input parity |
| B.2 KIFS | ✅ | 0f50a62 |
Menger + Sierpinski folds; two follow-up fixes (d91a6ab, 30a77d9) |
| B.3 Hybrid chain | ✅ | 96c310f |
UserBulb chain primitives |
| B.4 Kleinian | ✅ | 4316932 |
Tetrahedral 4-sphere preset only — see deferred section |
| C.1 Quat Julia | ✅ | 5b32fd2 |
|
| C.2 Quat Mandelbrot | ✅ | 89beab5 |
|
| C.3 Bicomplex | ✅ | 2532e3d |
Tessarine algebra inlined in calculator (no separate Bicomplex struct) |
| D.1 Apollonian | ✅ | d1261a9 |
|
| D.2 DLA | ✅ | cb81f1b |
Fixed-grid render only — see deferred section |
| D.3 Plasma | ✅ | 7ad0e32 |
|
| D.4 Flame | ✅ | 5 commits (0923d7d → 464d3e7) |
Variation library + tone-map + per-map palette + post-affine + presets |
| D.5 L-System presets | ✅ | 7c63333 |
Total: 19 new fractal types landed since the roadmap was written.
These items are out of scope for the now-complete recommendation table but remain useful follow-ups. Capture here so a later session can pick them up without re-deriving context.
-
Theme compatibility matrix audit. New families (A.1–A.7, B.1–B.4,
C.1–C.3, D.1, D.2) were added without a sweep of the theme-gating table.
Verify that each family's theme set matches the defaults in the existing
rules (smooth-iter + distance on escape-time; density on A.7/D.2/D.4;
3D Phong on B./C. with DE). Concretely: enumerate
IColorMapentries, walk each newFractalType, check the family-tag set actually gates correctly in the theme picker, and note any rules that need extending. - Region preset coverage audit. Roadmap target was ≥ 1 built-in region per family. Most slices ship 1–2; spot-check the count and add missing presets for any family that's bare (visual: open the Regions panel, filter by family). Total built-in regions added this round: ~25.
-
Math help tab two-level grouping. Roadmap called for two-level grouping
once count > 25. Current count is ~34 sub-tabs in
HostHelpContentProvider- matching WinForms FloatingHelp. Group by family (escape-time / fold / 4D / geometric / stochastic) so the tab strip stops scrolling off the edge of typical window widths.
- FEATURES.md "20+ fractal families" line. Bump to ~38 (existing 20 + 19 new). Same for the README badge counter.
-
CalcGen reach verification. A.1 (Magnet 1), A.2 (Magnet 2), A.5
(Glynn), A.6 (Spider) should auto-flow through the CalcGen 5-path
generator if their kernel shape matches
f(z, c). Verify per kernel: bailout radius differs (10² for Magnet vs the usual 4); cardioid-skip likely off for these. If a path is missing, decide whether to add the generated calculator or document the family as scalar-only.
-
B.4 Kleinian.
- User-editable inversion-sphere list (currently hard-coded tetrahedral 4-sphere).
- Alternate Schottky configurations: necklace (Indra's Pearls "tree" / "limit-circle" presets), Klein-bottle 6-sphere, Apollonian-extrusion (gasket-style limit set built from a circle inversion stack).
- Full Möbius-group composition path so users can compose arbitrary inversion+rotation sequences and view the limit set of the resulting group, not just the inversion-only path the current calculator runs.
- True analytic DE (vs the inversion-scale heuristic) for crisper cusps under deep zoom.
-
D.2 DLA.
- Cached-blit pan/zoom: keep the produced grid, recompose the colour
buffer when only
CenterX/Y/Zoomchange so the user can frame the aggregate without paying the simulation cost again. - Pan/zoom-aware live re-sim (continuous-domain DLA): expensive, deferred indefinitely — only worth doing if the cached-blit path proves insufficient for the user.
- Multi-seed DLA: place several seed cells (e.g. tetrahedral on the grid corners) and let the aggregates collide. Trivial extension.
- Sticky-coefficient mode: probability < 1 of sticking on contact, walks past attached cells. Lower stickiness → bulkier aggregate (less branched). Worthwhile parameter for visual variety.
- Cached-blit pan/zoom: keep the produced grid, recompose the colour
buffer when only
-
C.3 Bicomplex. Visual differentiation against quaternion-Mandelbrot is low on most slices (roadmap noted this up front). If a clearer visual identity is needed, expose the second slice axis (currently hard-pinned to the k component) so the user can pick which 4D axis routes to the slice constant. Also: split-complex / coquaternion variant (k² = +1, ij = -ji = k — non-commutative) reuses the same raymarcher with a swapped product table.
-
B.2 KIFS. Only Menger and Sierpinski fold tables ship. Mandelbox- with-rotation, Octahedron, Dodecahedron folds all fit the same
KifsFoldKindenum. Each is one struct field + one switch arm. -
D.4 Flame. Eight variations of the Apophysis stock 49 ship. Adding more is mechanical (extend
FlameVariation+ApplyVariation). Slice 4 of the originally-planned 3 would add the next 8–16 most-used variations and ship them as preset library updates. -
D.1 Apollonian. The (−1, 2, 2, 3) seed packs the curvilinear cusps between the seed circles but does NOT generate circles inside the seed circles themselves — that is a property of the gasket definition, not an algorithm bug. If a "filled" rendering (sub-gaskets inside each disk) is desired, a separate seeding pass per disk would reproduce the integral packing recursively. Likely not worth the complexity vs the canonical gasket image users expect.
-
D.5 L-System. Five new presets shipped (Pythagoras tree, Dragon, Hilbert, etc.). The roadmap's full preset list called for ~10. Adding more is preset-JSON only, no code.
These were ruled out in the original roadmap and remain so:
- Mandelbar (= Tricorn, already shipped)
- Cubic / Quartic Mandelbrot (covered by Multibrot exponent param)
- Strange-attractor variants (already shipped under StrangeAttractor)
- Buddhabrot variants (extend existing Buddhabrot, not new family)
- Pickover stalks, orbit traps (coloring, not fractals; live in theme)
- Cantor set, Koch curve standalone (L-System covers)
-
No allowlist failure tests for the new types yet. All 19 new types
pass
AllowedTypes_AreAllowedbut there is no negative test for any new type — the negative path only coversUserEquation/Sandbox/UserBulb. Probably fine because the allowlist is exclusion-based, but a single "negative test for a non-existent fractal name" would catch regressions where someone accidentally blocks a built-in. - No headless visual-regression baseline. The smoke renders run in CI as build-only; a per-type golden PNG (hashed pixel-count by colour bucket) would catch silent visual regressions. Worth doing once the test infrastructure for image-fixture comparisons lands.
-
CLAUDE.md UI-policy bypass risk.
FractalParamsView.axamlhas grown to ~600 lines of per-type IsVisible-gated panels. A future refactor could extract per-type user controls into separate*ParamsControl.axamlfiles. Not urgent — current layout works, just reads dense.