Detailed DD atlas ↗
Numerical radial survey Angular parameter chart Drag to orbit · scroll to zoom · double-click to reset
ΠDD w0.500 α0.000π γ0.250π ρ1.4142
Try this example
Preparing the numerical survey…
The smooth mesh interpolates the finite radial survey. Display refinement adds no numerical evidence and does not establish locus topology.
Synchronized witness

The planar attractor

finite survivor
1×
Drag to pan · scroll to zoom
Deterministic finite approximation; display markers are distinct from audit enclosures.
Explore

Choose a mathematical family

Vary both complex multipliers independently, or enter a named family to explore its own coordinates.

Four-dimensional coordinates

λ₋ = (2w/ρ)eⁱ⁽ᵅ⁻ᵞ⁾   ·   λ₊ = (2(1−w)/ρ)e⁻ⁱ⁽ᵅ⁺ᵞ⁾

Angles in radians. ρ₂(w) = 2√(w² + (1−w)²) is the area-critical reference, not a connectedness test.

rad
rad
Enter complex multipliers

Apply all four components together. The selected orientation family is retained; numerical entries are not exact certificates.

Drawing overlays

Research notebook 0 saved

Save named parameter states in this browser and export a portable JSON collection.

Numerical evidence
Computing selected parameter…

The finite test and image resolve independently.

Display depth —Test depth —Max. tail radius —

Finite survival means unresolved. Browser arithmetic supplies numerical evidence. The separate rational verifier checks explicit cylinder covers and disconnected parameter neighbourhoods.

Reproducible figures

Export current view

The figure is rendered again at the chosen resolution. Exact numeric parameters, computation limits and view settings are embedded in the PNG as JSON.

High-resolution geometry uses the displayed deterministic points and depth. Other depth options rebuild finite attractor cylinders. Inspection bounds are preserved when exporting the current region. Angular surveys, marked differences and contact graphs retain their actual computed resolution. Export never upgrades evidence to a theorem.
Classified collection

Landmark catalogue

Load a reference parameter or compare up to three finite approximations.
Evidence dossier

Finite survivor

Reference classification and finite contact data

Finite computation

Canonical specialization

Source and caveats

What the interface may say

  1. Exact theoremAnalytic classification or exact landmark.
  2. Numerical exclusionAll tested enclosures are pruned; exact replay is required.
  3. Finite survivorUnresolved — never relabeled connected.
  4. ProgrammeStructural interpretation under explicit hypotheses.
Field guide

Definitions, controls and sources

Controls

  • Drag the torus to orbit; use Phase map for explicit angular coordinates and sampled-radius colour.
  • In the dynamical plane, drag to pan, scroll or use +/− to zoom, and Fit or the 0 key to reset. The arrow keys pan. Target 2 inspects the marked-difference neighbourhood.
  • The Research notebook stores named parameters locally and imports or exports a JSON collection.
  • Use the six lenses to keep one parameter while changing representation.
  • Press ← and → to move through the journey.
  • Press 1–6 for Angular chart, Attractor, Marked difference, Symbolic structure, Catalogue and Evidence.
  • Use Learn for the introduction, Focus for a larger figure, or Workspace for precise controls.
  • Press E for the parameter inspector, ⌘/Ctrl-K for navigation, and ? for this guide.

Terminology

Sources and scope
Structural comparison

Compare without losing the shared coordinates
Navigate the atlas

Go to a concept, view or landmark