A linked numerical study · DD · w = ½
From the atlas to the fractal
Choose a point on the coloured surface. Read its two first-level pieces beside the marked difference that carries their contact problem.
Loading the six specimens…
Ring markers in K: the fixed points of f₋ and f₊.
The contact question is 2 ∈ Dp. Hulls and opacity help read the finite geometry; a rendered overlap does not decide this limiting membership.
Detail for these two images
Read the figure precisely
One parameter, several kinds of evidence
The attractor is generated by f₋(z) = −1 + λ₋z and f₊(z) = 1 + λ₊z. On this equal-contraction slice, λ₋ = ρ⁻¹ exp(i(α−γ)) and λ₊ = ρ⁻¹ exp(−i(α+γ)).
The hull outlines come from the finite addressed centres; ring markers show the branch fixed points. The views are fitted independently, with one-unit scale bars. Difference opacity represents the probability of independent, uniformly chosen finite words on the stated lattice, computed by histogram cross-correlation with word multiplicities retained. Each of λ₋x and λ₊y is rounded to the lattice before taking their difference. It is neither a density of the limiting measure nor an estimate of dimension. The torus is a display of angular coordinates.