Goodwin & Whitworth (2004)

Abstract (paraphrased)¶

Simulates the dynamical evolution of fractal star clusters (generated by a recursive box-fractal tree, parameterised by a single fractal dimension $D$) to ask how long initial substructure survives. The velocity dispersion is the key control: clusters with virial ratio $Q_\mathrm{vir}\equiv T/|V|\gtrsim0.5$ retain their initial density substructure for several crossing times in virtually all cases, whereas low-velocity-dispersion (cold, sub-virial) clusters erase it during the ensuing collapse. Even an initially homogeneous cluster can develop substructure if it is born with coherent velocity dispersion. (Verified against the held PDF, A&A 413, 929, abstract

• §1–2; 2026-06.)

Use in progenax¶

• Fractal substructure — GW04 algorithm + the fractal-dimension $D$ ↔ CW04 $Q$ relationship (theory)

• Substructure (CW04 Q) validation — current substructure-validation status (CW04 $Q$ diagnostic)

Notes¶

The standard fractal IC and the source of the fractal-dimension $D$ parameter. progenax’s differentiable Fractal Displacement Field replacement (cluster.fdf, cluster.fractal_gw_legacy) was removed in the 2026-06 clean-room rewrite and has no released successor; GW04 now appears only as theory pedagogy and as the fractal-dimension ladder behind the CW04 $Q$ diagnostic (the surviving substructure tool). Turbulent-density ICs are now the experimental gravoturb package (a density-field method, distinct from the GW04 displacement fractal).