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Laboratory / direct similarities

A landscape of possibilities.

Move through the parameter landscape and watch its fractals transform. Six movable locators connect the survey to high-resolution views of Kₚ and Dₚ, with finite evidence close at hand.

Finite numerical survey43,173 rays · 13 × 41 × 81 grid · depths 9 and 10. This detailed direct-similarity survey samples 0.35 ≤ w ≤ 0.65, 0 ≤ α ≤ π/2 and 0 ≤ γ ≤ π. The torus repeats that angular sector; use the live atlas for the full angular domain.

Direct similarities (f₀, f₁): f₀(z) = −1 + az and f₁(z) = 1 + bz, with a = λ₋ and b = λ₊. The laboratory samples M = Mff. Orientation types, slices and marked stability ↗

Dataset and evidence scope
43,173sampled parameter rays
13weights between 0.35 and 0.65
—finite fingerprint components
—secondary radial components
—weight-persistent candidates
384 × 768maximum GPU display mesh

The numerical survey contains 13 sampled weights from 0.35 to 0.65 and a 41 × 81 angular grid. Angular cosine interpolation and a cubic spline in weight smooth the sampled outer exits; a finer display mesh does not add survey samples. Agreement between depths and apparent persistence are diagnostics; neither provides an interval certificate or proves a limiting topological feature.

Route objective weights and endpoints

Angular parameter atlas

Drag to orbit · wheel to zoom · move a locator to inspect · double-click the surface to travel
Outermost sampled exit

Attractor · finite prefixes

Unequal branch ratios, deterministic prefixes, visible tail radius and finite status
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Radial survival bands

Every finite survival loss and re-entry is retained instead of assuming radial monotonicity
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Finite contact structure

Noncrossing chord core, paired prefixes and work-cap status
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Reproducibility record · state and numerical evidence