{
  "schema": "connectedness-atlas/curated-study/v1",
  "title": "Attractors and contact differences",
  "provenance": {
    "author": "Bernat Espigulé",
    "date": "2026-09-16",
    "family": "DD",
    "weight": 0.5,
    "attractorDepth": 22,
    "atlasSymbolicTailDepth": 24,
    "atlasCylinderLength": 25,
    "description": "Six finite numerical parameter samples from the equal-contraction angular atlas.",
    "hullScope": "Finite convex hulls; their containment test is weaker than exact contact.",
    "densityScope": "Finite empirical raster density; no density of the limiting measure is asserted.",
    "topologyScope": "Atlas hue encodes a selected finite pair-address code, not a topological equivalence class.",
    "imageProjection": "Toroidal display of parameter coordinates; its central hole is imposed by the display."
  },
  "camera": {
    "imageSize": [
      6000,
      4500
    ],
    "screenUVOrigin": "top-left",
    "coordinateFormula": "((4+rho*cos(alpha))*cos(gamma),rho*sin(alpha),(4+rho*cos(alpha))*sin(gamma))"
  },
  "display": {
    "pieceColors": [
      "#D23B3B",
      "#2469B5"
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    "hullColor": "#657b89",
    "differenceDensity": {
      "transform": "log1p",
      "reference_definition": "Maximum of the six per-pin 99.5th percentiles over positive physical density pixels; shared by every displayed pin.",
      "formula": "opacity = clip(log1p(density / softening) / log1p(density_ref / softening), 0, 1)",
      "zero_density_opacity": 0,
      "same_across_pins": true,
      "note": "This nonlinear contrast is a display choice; the stored probability density is untransformed.",
      "density_ref": 0.47515467926859856,
      "softening": 0.004751546792685985
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    "imageBoundsOrder": [
      "xmin",
      "xmax",
      "ymin",
      "ymax"
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    "imageTop": "ymax",
    "scaleBarUnits": 1,
    "viewsFittedIndependently": true,
    "overview": "assets/atlas-overview.png",
    "overviewHighResolution": "assets/atlas-overview-6k.png"
  },
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      "code24": "271580177957632",
      "w": 0.5,
      "family": "DD",
      "images": {
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        "D": "assets/A-D.png"
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        "hullScope": "Convex hull of unrounded finite centres; exact-arithmetic Hausdorff bound to the filled limiting convex hull. Numerical floating-point construction.",
        "target": [
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        "density": {
          "transform": "log1p",
          "reference_definition": "Maximum of the six per-pin 99.5th percentiles over positive physical density pixels; shared by every displayed pin.",
          "formula": "opacity = clip(log1p(density / softening) / log1p(density_ref / softening), 0, 1)",
          "zero_density_opacity": 0,
          "same_across_pins": true,
          "note": "This nonlinear contrast is a display choice; the stored probability density is untransformed.",
          "density_ref": 0.47515467926859856,
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          "units": "probability per square complex-coordinate unit",
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          "definition": "Histogram of independent uniform choices of length-22 addressed centres; original word multiplicities are retained."
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      }
    }
  ]
}